Vaughan was accused of saying "there's too many of you lot, we need to have a word about that" to Rafiq and three other Asian players representing Yorkshire in 2009.
The Cricket Discipline Commission (CDC) panel found the England and Wales Cricket Board's case against Vaughan, 48, was not proved.
The panel said it was "not satisfied on the balance of probabilities" that the words were said by Vaughan "at the time and in the specific circumstances alleged".
It said there were "significant inconsistencies" in the evidence provided by Rafiq and fellow key witness Adil Rashid regarding the exact wording of Vaughan's alleged comment.
It added its findings "do not in any way undermine" Rafiq's wider evidence - in which he said English cricket is "institutionally racist".
The panel said the case did not need a conclusion that "anyone had lied or acted out of malice".
It said it "had to consider whether the case as presented to it by the ECB... was sufficiently accurate and reliable, on the balance of probabilities, to rule out mistake. It was not."
The CDC panel, chaired by Tim O'Gorman, upheld some of the charges against former Yorkshire players Tim Bresnan, Matthew Hoggard, Andrew Gale, Richard Pyrah and John Blain - all of whom withdrew from the process.
Rafiq alleged Vaughan made the comment to him, Rashid, Rana Naved-ul-Hasan and Ajmal Shahzad before a match against Nottinghamshire at Trent Bridge on 22 June 2009.
Vaughan was charged, along with Yorkshire County Cricket Club and six other former players, with bringing the game into disrepute following a nine-month investigation by the ECB - English cricket's governing body.
Yorkshire previously accepted four amended charges. In a statement, interim chair Baroness Tanni Grey-Thompson and chief executive Stephen Vaughan said: "As a club, we needed to accept and take accountability for the cultural issues which allowed racist and discriminatory behaviour to go unchallenged."
Former England batter Gary Ballance also previously admitted the charge against him.
Ashes-winning captain Vaughan, who led England in 51 Test matches between 2003 and 2008, was the only respondent to appear at the CDC hearing at the International Arbitration Centre in London from 1-9 March.
All parties have 14 days to appeal against the CDC's decisions. The panel will disclose the sanctions against the individuals and the club at a later date.
BBC pundit Vaughan - in a statement posted on social media before the ruling was officially released - said: "It has been both difficult and upsetting to hear about the painful experiences which Azeem has described over the past three years.
"The outcome of these CDC proceedings must not be allowed to detract from the core message that there can be no place for racism in the game of cricket, or in society generally."
He added: "I have never wanted to do anything that runs contrary to genuine efforts to clean up the game of cricket. I truly hope people can understand why, on a personal level, I could not just accept, or apologise for, something which I know I did not do.
"At times, this process has brought me to the brink of falling out of love with cricket. I won't address here the toll that it has taken on me and my family, but I have no doubt that it has also been incredibly stressful for all of the others concerned. I hope that for them and for cricket, an inclusive healing process can now begin."
Rafiq said: "The issue has never been about individuals but the game as a whole. Cricket needs to understand the extent of its problems and address them.
"Hopefully, the structures of the game can now be rebuilt and institutionalised racism ended for good. It's time to reflect, learn and implement change."
Richard Thompson, ECB chair, said: "This has been an incredibly challenging period for our sport, but one we must all learn from in order to make cricket better and more inclusive.
"Given the nature of these cases, they have taken a clear toll on everyone involved. There now needs to be a time of reconciliation where, as a game, we can collectively learn and heal the wounds and ensure that nothing like this can ever happen again."
The Independent Commission for Equity in Cricket is expected to deliver its findings soon.
It was set up by the ECB in 2021 to consider matters of race, class and gender within cricket and make recommendations on improving inclusivity in the sport.
Vaughan retired from playing in 2009 and went on to work as a summariser on BBC radio programme Test Match Special. He stepped back from the role in June 2022.
A BBC spokesperson said: "We note the findings by the Cricket Discipline Commission in relation to Michael Vaughan. Michael is not currently under contract with the BBC, although we have remained in touch with him throughout the process. At this stage, we won't be commenting further."
Sport anti-racism campaign group Kick It Out said the CDC process had been "a difficult but necessary step in the process of helping cricket heal and reform".
It praised Rafiq's "great courage" during what had been "a bruising episode for the game" but said it had already been in contact with the ECB to offer suggestions "about addressing cricket's culture, how it can begin its process of reconciliation and what practises can be in place to better support players".
Former Yorkshire bowler Rafiq first made claims of historical racism at Headingley in August 2020 and in a Wisden article that month claimed a team-mate had made the alleged comment, but did not name Vaughan.
An independent investigation commissioned by Yorkshire upheld seven of Rafiq's 43 claims in September 2021, but the full report has never been published and the club said no player, employee or executive would face disciplinary action as a result of its findings, sparking widespread criticism.
The ECB began its own investigation in October 2021 and the following month Yorkshire were temporarily stripped of the right to host international matches, chairman Roger Hutton and chief executive Mark Arthur resigned, and several sponsors ended their partnerships with the club.
Vaughan revealed he was named in the report in November 2021 and denied the allegation.
Later that month - in an emotional testimony before a Digital, Culture, Media and Sport select committee in which he called English cricket "institutionally racist" - Rafiq said of Vaughan: "It's important on Michael that we don't make it all about Michael."
Giving evidence at the CDC hearing, Vaughan was critical of the ECB investigation, calling it "a terrible look for cricket" and said he "knows" he did not make the alleged comment because he was "proud" of it being the first time four Asian players had been in the same Yorkshire side.
He also denied having heard racial slurs while at Yorkshire.
Vaughan did apologise for sending "disgusting" historical tweets which were first brought to his attention in a 2021 BBC interview. ECB lawyer Jane Mulcahy KC argued the tweets showed it was "inherently probable" Vaughan made the alleged comment.
Vaughan's lawyer Christopher Stoner KC drew attention to discrepancies in Rafiq's evidence, including Rafiq telling the initial investigation that Vaughan said "there's too many of you lot, we need to do something about it".
Rafiq took "full responsibility" for the mistake but said he "clearly" recalled Vaughan making the comment insisting the former batter did say the phrase "there's too many of you lot".
England spinner Rashid and former Pakistan bowler Naved-ul-Hasan corroborated Rafiq's claim. Former England bowler Shahzad said he had no recollection of it happening.
Giving evidence via video link from Bangladesh on an England tour, Rashid said he had a "very clear recollection" of Vaughan making the comment and denied he had been "pressured" by Rafiq into corroborating the allegation.
Stoner called the ECB investigation "woefully inadequate" and criticised the governing body for not speaking to all the other Yorkshire players taking part in the match, the Sky cameraman and the umpires.
The ECB strongly denied an accusation of bias against Vaughan by Stoner, adding it was "inappropriate" to make that allegation.
Stoner said the case was "so critical" to Vaughan because "the shape of his life and his livelihood is at stake".
Part of the hearing took place in public - a first for the CDC - following a request from Rafiq. The proceedings were delayed until this year after "a number of the respondents" appealed against the decision to hold them in public, but those appeals were all dismissed.
Hoggard, Bresnan and Blain all withdrew from the disciplinary process on 3 February 2023, believing they would not get a fair hearing.
Pyrah withdrew on 7 February 2023, while Gale withdrew on 29 June 2022, calling it "tainted".
On the charges that were upheld, the panel said it was "satisfied on the balance of probabilities that the conduct as alleged occurred".
Former England bowler Hoggard was charged with using two racial slurs as well as referring to Rafiq and other Asian players in the Yorkshire squad as "you lot", which he denied.
He had previously admitted using a term that is racially offensive in South Africa, but denied any racist intent.
The panel found the allegation the 2005 Ashes winner used the term "you lot" not proved.
However, regarding the use of the other two racial slurs, the panel found the charges proved.
Former England bowler Bresnan was charged with using a racial slur relating to Pakistani heritage towards Rafiq's sister Amna during a media day at Headingley in 2014, and subsequently towards other Asian women.
He was also accused of using the terms "the brothers" and "you lot" to specifically refer to groups of Asian players.
Two-time Ashes winner Bresnan denied all the allegations and said had never met Amna Rafiq, stating he had only seen her from afar when she was working at Leicester.
The panel said the allegations Bresnan used the terms "brothers" and "you lot" were not proved.
However, it found the allegation he used a racial slur towards Amna Rafiq and other women proved.
Former Yorkshire coach Blain was charged with using a racist phrase to describe Asian individuals during pre-season training at Headingley in 2010, as well as on other occasions at Yorkshire during that year and 2011.
Blain denied the allegation.
The panel found the charge proved.
Former Yorkshire bowling coach Pyrah, who withdrew from the process on 7 February 2023, was accused of using the same racial slur as Bresnan towards Rafiq's sister, as well as the term "you lot" towards groups of Asian players, both of which he denied.
As with Bresnan, the allegation Pyrah used the term "you lot" was not proved.
However, it found the allegation he used a racial slur towards Amna Rafiq and other women proved.
Former Yorkshire captain and head coach Gale was charged with using two racist slurs towards Rafiq throughout his time at the club, as well as using one of these racist terms towards Mosun Hussain, a Yorkshire academy player, in 2013. He denied the allegations.
The panel found both charges proved.