The DJ, 33, will step down in September and will be replaced by Greg James.
It comes two weeks after figures revealed that Grimshaw’s show had the second lowest audience ratings since current records began.
He 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.”
Grimshaw said he would remain with the station on the drivetime show, swapping jobs with James.
He added 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.”
The broadcasters are scheduled to start their new roles this autumn.
Following the announcement, Grimshaw joked that he “ain’t had a good night’s sleep since God knows when”.
He added that he has had “jet lag for six years”.
His programme pulled in 5.1 million listeners a week in the first quarter of 2018, compared with 5.7 million a week in the last quarter of 2017, according to audience research body Rajar.
Grimshaw is the second-longest running breakfast show presenter in the station’s history behind Chris Moyles.
James said in a statement: “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.”