Comey, who was fired by Trump in 2017 after allegedly resisting the president's entreaties to drop an investigation into former national security advisor Michael Flynn, wrote the memos after meeting Trump during his early days at the White House.
One memo said the president asked Comey to shut down an investigation into Flynn, who eventually admitted lying to the FBI about conversations with Russia's ambassador.
The admission led to one of the earliest indictments to come from special counsel Robert Mueller's investigation into contacts between Russia and the Trump 2016 election campaign.
The Justice Department's Office of Inspector General berated Comey for asking an acquaintance teaching at Columbia University to share the contents of the memo with The New York Times.
Comey set a "dangerous example" for FBI employees in an attempt to "achieve a personally desired outcome," the report states.
But it found "no evidence that Comey or his attorneys released any of the classified information contained in any of the memos to members of the media" and said prosecutors had declined to bring a case.
Comey, who was among 17 people interviewed by the IG's office for the investigation, immediately responded on Twitter, saying a "quick message with a 'sorry we lied about you' would be nice."
Comey singled out the president, who has repeatedly upbraided the former law enforcement official as a "leaker" since details of the memos emerged.
"And to all those who've spent two years talking about me 'going to jail' or being a 'liar and a leaker' -- ask yourselves why you still trust people who gave you bad info for so long, including the president," Comey said.
Trump, who countered with his own take on the report, appeared unprepared to accept that it had vindicated the former FBI chief in any way.
"Perhaps never in the history of our Country has someone been more thoroughly disgraced and excoriated than James Comey in the just released Inspector General's Report," the president tweeted.
"He should be ashamed of himself!"
In a statement, the White House charged that Comey "disgraced himself and his office to further a personal political agenda."
"Because Comey shamefully leaked information to the press -- in blatant violation of FBI policies -- the nation was forced to endure the baseless politically motivated, two-year witch hunt," the statement from press secretary Stephanie Grisham said.
The IG focused on Comey's handling of seven memos detailing interactions with Trump in the first three months of 2017. Comey kept signed originals of four memos at home after being fired, without telling the FBI.
He also gave copies of several memos to personal attorneys and to Mueller's team, the report said.
"Department policy states that employees may not, without agency permission, remove records from the Department -- either during or after employment," the report said.
"The FBI policies are no different.