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 starts his new role representing Utah 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 on Wednesday taking aim at Romney's failed 2012 White House bid.