Latest: House Speaker Paul Ryan said Mr Trump did not consult him on his choice of Mr Wray. But he said the lawyer seems "the perfect kind of person" to succeed Mr Comey.
Mr Ryan said he favoured a "career person" to take over the FBI, and Mr Wray "certainly seems to fit that bill".
Earlier: President Donald Trump has announced he will nominate a former Justice Department official as FBI director.
In a tweet outlining his choice, Mr Trump said lawyer Christopher Wray is "a man of impeccable credentials".
I will be nominating Christopher A. Wray, a man of impeccable credentials, to be the new Director of the FBI. Details to follow.— Donald J. Trump (@realDonaldTrump) June 7, 2017
Mr Wray emerged from a list of former prosecutors, politicians and law enforcement officials interviewed by Mr Trump since he fired FBI director James Comey last month.
Mr Wray works at the King & Spalding law firm.
He represented New Jersey governor Chris Christie during the investigation into the George Washington Bridge lane-closing case. Two former Christie aides were convicted of plotting to close bridge lanes to punish a Democratic mayor who would not endorse the Republican governor.
Mr Wray worked for the Justice Department under President George W Bush.
Mr Trump's announcement came one day before Mr Comey gives evidence in public on Capitol Hill for the first time since his dismissal.
During his appearance before the Senate intelligence committee, Mr Comey is expected to describe his encounters with the president in the weeks before he was fired on May 9.
Mr Comey could offer new details regarding discussions with Mr Trump about the federal investigation into Russia's election meddling.