Writing in the Washington Post, he said Trump had not “risen to the mantle” of the presidency.
Romney has been fiercely critical of Trump before but won his backing for his run in Utah.
There has been no response yet from the US president.
He has previously attacked Romney as a “failed candidate” and his manager for the 2020 presidential campaign accused him of jealousy.
The timing of the article, just two days before Romney is sworn in, prompted some to speculate he was positioning himself as a challenger to Trump securing the Republican presidential nomination.
In the article, Romney praised many of Trump’s policies, such as his tax reforms and appointment of conservative judges, ones he said “mainstream Republicans have promoted for years”.
But he went on to say: “With the nation so divided, resentful and angry, presidential leadership in qualities of character is indispensable. And it is in this province where the incumbent’s shortfall has been most glaring.”
“The world is also watching,” he added. “Trump’s words and actions have caused dismay around the world.”
Romney said he would support the president in policies he thought were in the best interests of Utah or the US but speak out against actions “that are divisive, racist, sexist, anti-immigrant, dishonest or destructive to democratic institutions”.
Romney’s article has been widely discussed and covered across US media. Several outlets suggested that Romney was positioning himself to be Trump’s leading critic in Congress.
The New York Times even said much of the essay “sounded like the makings of a primary challenge against Mr. Trump from Mr. Romney”.
On social media, some praised Romney, others said he should have gone further. Conservative commentators and pro-Trump writers have accused him of duplicity and opportunism.
During the 2016 campaign, Romney said Trump had neither “the temperament nor the judgement to be president” while Trump called Romney a “choke artist” and called his bid for the presidency in 2012 “the worst ever”.
The same year though, the pair met for dinner amid reports Trump was mulling appointing Romney as his secretary of state.
Romney has also taken issue with Trump labelling the press the “enemy of the people” as well as his response to a violent far-right rally in Charlottesville.
When US Congress reconvenes on Thursday, Trump faces a new challenge on the domestic front – in November’s mid-terms the Republicans strengthened their hold of the Senate but lost the House of Representatives. – BBC