The broadcaster, who hosts the Friday edition of the magazine show, will leave on July 10.
The news comes after the man he is replacing on Top Gear, former host Jeremy Clarkson, claimed he was offered a sensational return to the hit show days after Evans got the job.
Clarkson, axed in March for punching producer Oisin Tymon in a row over a steak dinner, told the Sun he met an unnamed BBC executive last week before Evans, 49, was unveiled as the new host.
But he said that he turned it down because of what had happened since his departure, including being compared to paedophile DJ Jimmy Savile.
Clarkson, 55, told the Sun: “I had a meeting with a BBC executive last week and they asked if I’d come back to Top Gear.
“But it was never an option, even with the one million people signing the Bring Back Clarkson petition - for which I was extremely humbled.
“Too much has gone on. After I’d been compared to Jimmy Savile by someone from the BBC and it was splashed all over a Sunday newspaper, how could I go back?
“The spotlight would have been on me and the show would end up being neutered. It would be difficult to do anything without interference. It would have been impossible to make the show I’d want to make.”
A BBC spokesman said: “We haven’t offered another Top Gear contract and the BBC had placed on record its thanks to Jeremy for his broadcasting on the programme and wish him well for the future.”
The BBC also announced today that one of Clarkson’s former colleagues, James May, will co-host another BBC motoring show and released pictures of the pair with Richard Hammond from their final Top Gear appearance.
May, who was unveiled today as the co-host of new BBC show Building Cars Live, was pictured with Hammond and Clarkson in a series of shots showing them behind the wheel of classic cars and beaten-up 4x4s in their final challenges as a trio.
Pictures were also released of scenes filmed in the studio with just May and Hammond after Clarkson’s exit from the show.
Evans, who was unveiled as the new face of Top Gear on Tuesday, has called on the show’s fans to apply for the job of co-hosting it with him.
The Radio 2 breakfast show DJ told candidates they needed to have an “appetite, hunger and need” to host the motoring show, and to send in videos of themselves from the waist up, with “no stunts, no gimmicks” or cars, behaving as they would if they were on the show.