Wray, 50, received an overwhelmingly bipartisan support -- 92-5 votes -- on the Senate floor.
"The FBI is our country's top law enforcement agency and it needs a qualified leader committed to upholding the rule of law and protecting its independence. I'm confident that Christopher Wray is up to that considerable task," said Senator Dianne Feinstein, Ranking Member of the Senate Judiciary Committee.
Mueller's team is investigating Russia's interference in the 2016 presidential election.
A former high-ranking official in President George W Bush's Justice Department who oversaw investigations into corporate fraud, Wray takes up the top job at a critical juncture marked by the ouster of Comey.
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Senate Democratic Whip Dick Durbin said the next FBI Director will be under incredible scrutiny.
"America needs an FBI Director who will face that pressure with integrity, independence, and a firm commitment to the rule of law," he said.
Wray is a proven public servant with an impressive law enforcement track record, and he is well-equipped to take the reins of the FBI during these challenging times, Senator Tom Carper said .
In a statement, Senator Ben Cardin, Ranking Member of the Senate Foreign Relations Committee, said Trump's firing of Comey and his continuing public criticism and intimidation of Attorney General Sessions and Deputy Attorney General Rod Rosenstein shows that "the President has little respect for the rule of law or separation of powers".
Cardin said it is outrageous that the Trump administration's decision to cancel the current request for proposals for a fully consolidated FBI headquarters puts America's national security at risk.