In his Twitter announcement, Trump described Wray as a "man of impeccable credentials."
Wray is a lawyer who was nominated by President George W. Bush to be the assistant attorney general in charge of the Department of Justice's criminal division in 2003. He served in that position until 2005 and then returned to private practice, specializing in white collar and internal investigations.
Wray will require Senate confirmation.
Thomas O'Connor, president of the FBI Agents Association (FBIAA), issued a statement today on Trump's pick for the next FBI director, saying the "FBIAA National Executive Board looks forward to meeting with Mr. Wray ... very soon."
"As the key stakeholder in this process, it is critically important that the FBIAA understands his views on the FBI, Special Agents, and the criminal and national security threats that Agents combat daily," O'Connor said in his statement.
Attorney General Jeff Sessions issued a statement today hailing Trump's nomination of Wray, whom he called a "brilliant legal mind."
"Chris Wray is an extraordinary person, possessing all the gifts necessary to be a great Director of the FBI. I congratulate President Trump for choosing a leader of proven skill, independence, and integrity, a man in whom all Americans can have confidence," Sessions said in his statement. "The President asked us to look for an FBI Director who has integrity, who understands and is committed to the rule of law, and who is dedicated to protecting the American people from crime, gangs, and terrorists. We have found our man in Chris Wray."
However, Wray's nomination came as a surprise to many on Capitol Hill.
Sen. Chuck Grassley, R-Iowa, chairman of the Senate Judiciary Committee, told ABC News that he first learned of Wray's nomination from the president's tweet this morning.
"I don't know [Wray], except when I had conversations with him 13 years ago," he told ABC News.
Grassley later said he believes Trump likely attempted to contact him about Wray's nomination before posting the move on Twitter.
"There wasn't any effort to avoid me," he said.
"The president told me a couple weeks ago that he was going to let us know ahead of time," Grassley told ABC News. "I believe that he probably tried to get a hold of me, but I wasn't available."
House Speaker Paul Ryan also appeared caught off-guard by Wray's nomination.
"Wray, right? I don't know the guy, but I've looked at his resume," Ryan told ABC News. "He seems like to me he's the perfect kind of person."
"I thought we should have a career person take over the FBI, someone with a deep bench of experience," Ryan added. "He certainly seems to fit that bill."
Sen. Dianne Feinstein, D-Calif., the top democrat on the judiciary committee, said she needs to learn more about Wray.
"He may be fine," Feinstein told ABC News. "I haven't known about it for very long, like two hours."
Sen. Richard Blumenthal, D-Conn., a member of the judiciary committee, said he was concerned about the "timing" of Wray's nomination, but was hopeful in his years of experience as an attorney.
"FBI nominee Wray has solid credentials -- now this job will require independence [and] guts to stand up to political interference," Blumenthal tweeted today. "Despite my concerns on Wray nomination timing, hopeful he will demonstrate the backbone to continue investigation -- essential for the role."
Republicans largely praised Trump's choice. Sen. Ben Sasse, R-Neb., said he looks forward to sitting down with Wray, while Sen. Orrin Hatch, R-Utah, touted Wray's "impeccable credentials, vast experience and strong support across the board."
Trump fired James Comey from the position of FBI director last month. Andrew McCabe, the deputy director of the FBI, was named acting director.
The White House later released the letter that the president wrote directly to Comey, which said his termination was "effective immediately" and cited recommendations of the United States attorney general and the deputy attorney general.
Comey's dismissal came just weeks after he testified in front of the House Committee on Intelligence, during which he took the rare step of confirming that the FBI was investigating alleged Russian interference in the 2016 U.S. presidential election and "any links between individuals associated with the Trump campaign and the Russian government and whether there was any coordination between the campaign and Russia's efforts."
ABC News' Mary Bruce, Mariam Khan, John Parkinson and Ali Rogin contributed to this report.