In a Washington Post essay published late on Tuesday, Romney suggested the US leader had "caused dismay around the world" and said his presidency had "made a deep descent in December."
"On balance, his conduct over the past two years ... is evidence that the president has not risen to the mantle of the office," said Romney, who takes up his new role in Washington on Thursday.
"The appointment of senior persons of lesser experience, the abandonment of allies who fight beside us, and the president’s thoughtless claim that America has long been a 'sucker' in world affairs all defined his presidency down," he wrote.
The White House did not respond to a request for comment, but Trump fired back in a tweet early Wednesday morning that took aim at Romney's failed bid for the White House in 2012.
Trump has not risen to the mantle of the office: Romney
"Here we go with Mitt Romney, but so fast! Question will be, is he a Flake? I hope not. Would much prefer that Mitt focus on Border Security and so many other things where he can be helpful. I won big, and he didn't. He should be happy for all Republicans. Be a TEAM player & WIN!" Trump wrote on Twitter.
The president appeared to reference outgoing US Senator Jeff Flake, one of the few Republican lawmakers who publicly spoke out against Trump and drew the president's wrath.
Representatives for Romney could not be immediately reached for comment to Trump's tweet.
Romney had excoriated Trump during the 2016 presidential campaign as a "fraud" who was "playing the American public for suckers." Trump shot back at the time, criticizing Romney's 2012 loss to Democrat Barack Obama.
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But the two appeared to bury their bitterness, with Trump briefly considering Romney for secretary of state after he won the 2016 presidential election and, in February 2018, endorsing Romney's run for the Senate.
It is unclear whether any other Republican lawmakers will feel emboldened to criticise Trump ahead of his 2020 re-election bid or whether Trump will face any serious challengers for the Republican Party's presidential nomination.
But in his essay on Tuesday, Romney sought to stake out a more independent position in his party and vowed to be a loud voice in Washington, which now includes a divided Congress as Democrats take control of the US House of Representatives following their November election gains.
"I will speak out against significant statements or actions that are divisive, racist, sexist, anti-immigrant, dishonest or destructive to democratic institutions," he wrote.
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