Ms Psaki has been involved in a string of head-to-head confrontations in the briefing room with Mr Doocy during her time as the lead spokesperson for the president.
“End of an era in the Brady briefing room! Good luck, (Jen Psaki)” tweeted Doocy on Friday.
Earlier in the day he had told Fox & Friends that he will miss Ms Psaki, who is expected to take up a job as host and analyst on MSNBC, although she has not confirmed her landing spot.
“I think so, yes. It is the end of an era, like you said Ainsley, because everywhere I have gone for the last year and a half I have people roll down their car windows to say, ‘Hey Peter you have to ask Jen about X, Y or Z,’” he said.
“She has never said I’m not going to answer on that topic and that’s been a big help to everybody that’s watching right now so we will miss that.”
Mr Doocy, who was once called a “stupid son of a b****” on a hot mic by Joe Biden, admitted Ms Psaki had made him a “better reporter” for the preparation he had to do to face her and praised her for never ducking Fox News.
“She has always called on Fox, every briefing, more than 220 of them, I think I saw somewhere, and we hope that continues with Karine Jean-Pierre,” Mr Doocy said.”
Ms Psaki will be replaced by principal deputy press secretary Karine Jean-Pierre.
She also said earlier in the week that she would miss her sparring with Mr Doocy and said that the p[air had “a very good professional relationship”.