Chaffetz spent years conducting investigations into Benghazi, created to attack Hillary Clinton, but has bristled at providing the most basic oversight of President Donald Trump.
As chairman, Gowdy would lead the House's oversight of President Donald Trump and investigate whether the president attempted to quash an FBI investigation into former national security advisor Michael Flynn.
A Chaffetz spokesperson later explained the somewhat odd tweet, saying that they are having trouble finding Comey.
Chaffetz' departure is likely to spark a battle over who replaces him as the head of the oversight committee that will once again pit the House Freedom Caucus against the establishment.
Rep. Jason Chaffetz said Thursday he will resign from Congress next month, a move that calls into question the future of the House Oversight Committee's investigation of President Donald Trump and his campaign's ties with Russian Federation. A lengthy probe could extend past the Trump presidency and could, potentially, open up a can of worms for top Democrats like the Clintons. Chaffetz announced on Facebook in April that he would not be running for reelection in 2018.More news: Trump reportedly asked Comey to consider imprisoning members of the press
More news: Top senator calls for removal of Turkey's US ambassador
More news: Senate Intelligence Committee to The FBI: Give Us The Comey Memos
Liberals said that he did not go after the incoming administration with almost the vigor used against the prior Democratic administration.
Chaffetz is now less than six months into his fifth term representing Utah's Third Congressional District, and has served as the chairman of the House Oversight and Government Reform Committee since January 2015.
He has not ruled out a run for Utah governor in 2020. The internal jockeying among House Republicans to succeed Chaffetz in that high-profile role kicked off Thursday, with at least three Oversight Committee members phoning members of the House Republican Steering Committee, which will select his successor. "I'm a little concerned-and I harken to what I was told a year ago-that a special session to address election law is not an adequate enough time to have a deliberative approach". I told voters I did not believe Congress should be a lifetime career. "I just haven't seen it".
U.S. Rep. Jason Chaffetz speaks with reporters at his home Thursday, May 18, 2017, in Alpine, Utah.
Chaffetz added: "After careful consideration and long discussion with my wife, Julie, we agree the time has come for us to move on from this part of our life".