The National Executive Committee (NEC) met on Saturday amid a police probe and a row over the release of membership numbers.
Party leader Humza Yousaf said a new working group would publish an interim report in June.
It will be followed by a full report ahead of the SNP's autumn conference.
Asked if the review would go far enough, Mr Yousaf told BBC Scotland: "It is important that the financial oversight that we are committed to improving comes from the external input as opposed to within the party."
Last week Mr Yousaf revealed that he had been unware until he became leader that the SNP's auditors had resigned more than six months ago.
The firm Johnston Carmichael quit last September, and there is concern the party may be unable to conduct an audit due in July.
On Thursday, the new SNP leader and first minister also said he only recently learned that the SNP had bought a luxury motorhome.
It was seized by police from outside a property in Dunfermline as part of an investigation into the party's finances.
Former SNP chief executive Peter Murrell, who is Nicola Sturgeon's husband, was also arrested on 5 April while their home was searched. He was later released without charge.
Mr Murrell resigned from his SNP position last month after misleading statements about party membership numbers were given to a journalist.
On Saturday the NEC approved proposals for the appointment of a new chief executive through an "open and transparent" external recruitment process.
Prior to the NEC meeting, one committee member had suggested he might resign unless "forensic auditors" were appointed to examine the party's finances. A forensic audit is used to uncover evidence that could be used in a court of law.
Bill Ramsay, the SNP trade union group convener, said: "I have been raising issues about the governance of the party for some time."
He added: "If the call to appoint forensic auditors is not moved forward, I will have to seriously consider whether I can continue on the NEC."
On Saturday Mr Yousaf dismissed speculation that the SNP could be facing bankruptcy. He replied: "It's not. The party is solvent."
The police investigation follows complaints about how the party spent more than £600,000 of donations that it received from activists to fund a future independence referendum campaign.
Questions were raised after accounts showed the SNP had just under £97,000 in the bank at the end of 2019, and total net assets of about £272,000.
Meanwhile, Mr Yousaf was in the Rutherglen and Hamilton West constituency on Saturday, where there is the prospect of a by-election.
Margaret Ferrier won the seat for the SNP in 2019 - but was later found to have damaged the reputation of the Commons and placed people at risk by taking part in a debate and travelling by train after testing positive for Covid-19. She now sits as an independent.
If she is barred from the Commons for 10 days or more, that could trigger a recall petition, which would result in a by-election in the constituency - although 10% of voters there would need to support this for it to go ahead.
Mr Yousaf told the BBC the party took "decisive action" against Margaret Ferrier at the time, which he supported.
He added: "We want there to be a by-election. We will support the recall petition.
"We have got a really strong track record, not just what we have delivered for this constituency but what we have delivered for the people of Scotland."