The announcement comes two weeks after new data revealed that Grimshaw’s show had recorded its second lowest audience figures since current records began.
His programme shed 600,000 listeners in the first quarter of this year, pulling in 5.1 million listeners a week in the first three months of 2018, compared with 5.7 million a week in the last quarter of 2017, according to audience research body Rajar.
Grimshaw, who took over the early morning radio programme in 2012 from Chris Moyles, said he’s “really tired” and had the position for much longer than he first thought he would.
The DJ told his listeners on Thursday morning: “Come September it will be six years... I’ve decided it’s time for a change, time for a new show and, most importantly, it’s going to be time for a new wake-up time... preferably about 11.30.”
He said he will remain on BBC Radio 1 on the drivetime show in a job swap with James.
The broadcasters will start their new shows on Radio 1 this autumn, the BBC has said.
This week, Grimshaw became the second-longest running breakfast show presenter in the station’s history, taking over from Tony Blackburn.
James has hosted the weekday 4pm-7pm drivetime slot on the station in 2012.
Grimshaw joked that he “ain’t had a good night’s sleep since God knows when” and that he has had “jet lag for six years”.
James appeared on the programme and admitted to feeling nervous about announcing his new role as the Breakfast Show presenter.
He told Grimshaw: “I did not sleep one hour last night just thinking about it... it’s too much.”
James added that it’s a “big challenge” and he’s “ready to give this a go”.
Grimshaw said in a statement: “I had the time of my life. I’ve decided it’s time for a change and a new show.
“I love Radio 1 and can’t wait to get on with the new time slot and the removal of all alarms from my house.
“I’m so happy to be swapping shows with my friend and yours Greg James, and can’t wait to wake up to him each morning. Not literally. Just on the radio. Unless he’s up for it.”
In a statement, James said: “I am completely beside myself that I’ve been given the chance to present the most famous radio show in the world.
“It really doesn’t get any bigger than this and I really want to build on the great work Grimmy has done.
“The listeners have become like mates during the 10 years I’ve been on air, so to be there when they wake up is a real honour.
“They’re always front and centre and this will of course be the case on the new breakfast show. It’s going to be the most enjoyable challenge I’ve ever undertaken and I can’t wait to get started.”
Ben Cooper, controller of Radio 1, 1Xtra and Asian Network, said: “Greg gets his childhood dream, Grimmy gets a lie-in and the Radio 1 audience gets two exciting new shows with the biggest and most popular youth presenters in the country.
“I’m so proud that Radio 1 produces and nurtures the best talent in the industry - I gave Greg his first show when he joined us from student radio and now he’s getting the most famous radio gig in the world - it’s going to be fantastic. Grimmy’s done a brilliant job reinventing the feel and tone of the breakfast show by connecting with new audiences in new ways in the digital age.”