The PM’s top team has been banned from appearing on the show since March but health secretary Matt Hancock will appear on the show on Monday.
Downing Street had clashed with the show’s producers over an incident during the 2019 general election campaign, when Johnson famously hid in a fridge to avoid an interview with Morgan.
The boycott was thought to have been driven by the PM’s outgoing adviser Dominic Cummings.
Cummings and communications director Lee Cain were both asked to leave Downing Street on Friday after allegedly briefing against the PM and his partner Carrie Symonds.
Morgan, who is known for his confrontational style and has repeatedly spoken out about the ban, tweeted on Sunday he “just had a call from Downing Street”.
It is not yet known if government ministers will appear on BBC Two’s Newsnight or Channel 4 News, which have also been boycotted by Johnson’s Cabinet in recent month.
The decision to appear on GMB follows an embarrassing episode for the government, in which Hancock was pursued by ITV journalist Nick Dixon.
The move is a clear sign Johnson is keen to reset his premiership and is drawing a line under an era heavily influenced by the two Brexiteers.
The two men were asked to leave after the PM concluded they were briefing journalists about Symonds and Allegra Stratton, who will soon be the face of new US-style question-and-answer sessions with journalists.
The PM is set to meet with Tory MPs this week to reassure them, following days of turmoil.
The Sunday Times reported Johnson will “attempt to get his premiership back on track” by establishing a policy board that will appeal to northern working class voters who helped Johnson win last year’s general election.
The paper said the group will be chaired by MP Neil O’Brien, who helped former chancellor George Osborne devise the Northern Powerhouse, and added Johnson will meet the Northern Research Group of MPs on Monday to listen to their concerns.
Charles Walker, vice chair of the 1922 committee of backbench Tory MPs, said the PM must “get the hires right”.
He told Times Radio on Sunday that Johnson needed “a chief of staff and two or three other people” as there was “a big job to be done at this time”.
Adding MPs had felt sidelined, he said: “But it’s just a feeling that there are people at Number 10 who are interested in what we think and want to relay what we think back to the Prime Minister who can’t always be in the tea room and around. We accept that. But, you know, Members of Parliament are not all idiots. I know we can be caricatured as idiots and that sells newspapers but we’re not. We’re deeply in touch with our constituencies.
Environment secretary George Eustice was asked about Cummings’ exit on Sky News on Sunday.
He told presenter Sophy Ridge that the former Vote Leave chief “tends to apply himself in short bursts”.
Eustice added that a new set of advisers, including the role of chief of staff, which is currently being filled temporarily by his long-standing ally Ed Lister, will be filled by the new year.
He said: “I’ve known Dominic Cummings myself for many years. He’s got many great strengths and one of them is winning campaigns.
“And he tends to apply himself in short bursts, short tours of duty, on big strategic changes such as the 2016 referendum result, such as the 2019 general election.
“And he’s very talented at that. But it’s always the prime minister’s prerogative who will be their key advisors.”
The prime minister’s official spokesman, James Slack, insisted Johnson was not being distracted by the row.