The ex-prime minister said Mr Johnson's decision to cut the overseas aid budget below 0.7% of national income had reduced the UK's global "credibility".
She told the Daily Mail the UK had to "live up to its values" and would be judged by its actions not its rhetoric.
The PM, meanwhile, has said he is looking forward to working "hand in hand" with new US President Joe Biden.
Mr Biden will be inaugurated as the country's 46th president on Wednesday, succeeding Donald Trump.
In advance of the historic day, Mr Johnson said he hoped the UK and US would join forces to address the most pressing challenges facing the world, which could only be tackled by "international co-operation".
But the PM's own record has come in for criticism from his predecessor as prime minister.
In an interview with the Daily Mail, Mrs May suggested the PM had squandered international goodwill by choosing not to meet the longstanding UN target of spending 0.7% of income on helping the poorest people on the planet.
The government says it cannot meet the figure this year because of the strain placed on the public finances by the pandemic and the billions spent on financial support.
But Mrs May said the UK's support for the 0.7% target, which is enshrined into UK law, and the commitment to also spend a minimum of 2% of income on defence set it apart from other nations.
She also criticised Boris Johnson's support for legislation which would have called into question the UK's commitment to uphold its legally-binding Withdrawal Agreement with the EU, had it been passed.
While controversial clauses were ultimately removed from the Internal Market Bill in December, after the UK and EU reached an agreement, Mr Johnson's threat to break international law caused considerable disquiet on the continent and in the US - where it led to warnings from Mr Biden against imperilling peace in Northern Ireland.
Mrs May said the UK was "well placed to play a decisive role in shaping this more co-operative world but to lead we must live up to our values".
"Threatening to break international law by going back on a treaty we had just signed and abandoning our position of global moral leadership as the only major economy to meet both the 2% defence spending target and the 0.7% international aid target were not actions which, in my view, raised our credibility in the eyes of the world.
"Other countries listen to what we say not simply because of who we are, but because of what we do. The world does not owe us a prominent place on its stage.
"Whatever the rhetoric we deploy, it is our actions which count. So, we should do nothing which signals a retreat from our global commitments."
Mrs May, who had a difficult relationship with Mr Trump, said Mr Biden's election presented the UK with a "golden opportunity" for Western democracies to reverse the trend towards "absolutism" in global affairs.
If the world was to bounce back from the pandemic, she said a spirit of compromise was needed and the era of a "few strongmen facing off against each other" had to come to an end.
2021 is seen as a pivotal year for the UK as it seeks to build its post-Brexit identity and deliver on the government's ambition of a "Global Britain" leading the world.
Mr Johnson, who will be centre stage as the UK holds the presidency of the G7 and hosts the Cop-26 UN climate summit in Glasgow, said he looked forward to welcoming Mr Biden to the UK at least twice this year.
"In our fight against Covid and across climate change, defence, security, and in promoting and defending democracy, our goals are the same and our nations will work hand in hand to achieve them," he added.
"Only through international co-operation can we truly overcome the shared challenges we face."
No 10 has declined to comment on Mrs May's comments.
“I am using the term “box tickers” to refer to employees who exist only or primarily to allow an organization to be able to claim it is doing something that, in fact, it is not doing.”
― David Graeber, Bullshit Jobs: A Theory