Gary Lineker Photo: AFP
Gary Lineker will return to present Match of the Day after he was taken off air following an impartiality row after he criticised the government's new asylum policy.
BBC director general Tim Davie said an independent review of BBC social media guidelines would be carried out - but denied the BBC had backed down.
Prime Minister Rishi Sunak said "it was right" the matter had been resolved.
But on Monday the BBC continued to face criticism from a range of sides.
Lineker said he supported the review and looked forward to getting back on air, describing the last few days as "surreal" and thanking people for their "incredible support".
Tory backbench MP Philip Davies told the Mail Online the BBC's decision was a "pathetic capitulation" to Lineker and the "start of the end for the licence fee", while ex-cabinet minister Jacob Rees-Mogg also warned the "licence fee has passed its sell-by date".
Labour's shadow culture secretary Lucy Powell, meanwhile, said the return of Lineker was welcome, but "much bigger questions remain about the impartiality and independence of the BBC from government pressures".
She said: "The ongoing uncertainties around the future of the BBC are keeping it over a barrel and making it susceptible to political campaigns orchestrated by ministers, MPs and the right-wing press.
"This saga should prompt the government to examine how it protects and promotes a truly independent and impartial BBC."
Liberal Democrat leader Sir Ed Davey tweeted the BBC "made the right decision".
Ex-BBC News executive Sir Craig Oliver, who went on to be a Downing Street communications chief under then-Prime Minister David Cameron, described the situation as "a total mess" and said it was the "wrong choice" to have asked Lineker to step back in the first place.
"The reality is the BBC today has announced it will have a review of its social media guidelines. In fact, it needs a review of how it handles crisis like these," he told the BBC.
Former controller of BBC editorial policy Richard Ayre said rewriting guidelines was not straightforward and was "going to be a nightmare".
"Whatever emerges will be unsatisfactory to a significant number of people. It's inevitable."
Ayre warned : "Gary will continue to hold his views. He says he will continue to abide by the BBC's guidelines until they're rewritten.
"But then, he was supposed to be abiding by the BBC guidelines last week when he tweeted what he tweeted. So watch this space, this story has a long way to run."
Earlier, Davie insisted the decision to pull Lineker off air was always about buying some time until the two sides could come to an agreement over his political tweets - and said that was exactly what had happened.
He said he took "proportionate action", adding: "We believe we did the right thing. I think I did the right thing."
The row began when, in a tweet, Lineker said the government's new Illegal Migration Bill was an "immeasurably cruel policy" and said the language used around it was "not dissimilar to that used by Germany in the 30s".
His words were criticised by Conservative ministers, including the home secretary.
Lineker was told on Friday to step back from presenting Match of the Day until an agreement was reached. It triggered an unprecedented wave of walkouts from fellow pundits and commentators in solidarity which disrupted weekend football coverage across the BBC.
On Monday, Davie said: "Everyone recognises this has been a difficult period for staff, contributors, presenters and, most importantly, our audiences.
"I apologise for this."
After announcing he will return to presenting on BBC TV, Lineker tweeted: "However difficult the last few days have been, it simply doesn't compare to having to flee your home from persecution or war to seek refuge in a land far away.
"It's heartwarming to have seen the empathy towards their plight from so many of you.
"We remain a country of predominantly tolerant, welcoming and generous people."
Lineker has hosted Match of the Day since 1999 and is the BBC's highest paid star, having earned about £1.35m in 2020-21. He is employed by the BBC on a freelance basis.
'Abide by the guidelines'
BBC employees are expected to remain impartial on political matters and must follow strict social media guidelines, but there is significant debate about how they should apply to staff outside of news.
Lineker said he backed the independent social media review which Davie said will have a "particular focus" on how the guidelines apply to freelancers outside news and current affairs.
"Shortly, the BBC will announce who will conduct that review," Davie said. "Between now and when the review reports Gary will abide by the editorial guidelines, that's where we are."
Lineker is expected to return to host Match of the Day's live coverage of the FA Cup quarter-final between Manchester City and Burnley on Saturday evening.
He is then set to front Sunday's live coverage of Grimsby Town at Brighton & Hove Albion on BBC One.
Davie added: "Gary is a valued part of the BBC and I know how much the BBC means to Gary, and I look forward to him presenting our coverage this coming weekend."
BBC Scotland confirmed it will have full coverage of Monday evening's Scottish Cup tie between Falkirk and Ayr United; after its programming was also limited over the weekend.
The BBC Board has welcomed the agreement with Lineker following the weekend of disruption.
In a statement the board said: "We believe this is the right time to look at the clarity of the BBC's social media guidance and how it is applied.
"We will support the executive in its continuing work to ensure the organisation delivers world-class, impartial content for all audiences."
Sunak also commented on BBC chairman Richard Sharp whose appointment is being investigated over his relationship with Boris Johnson. He denied wrongdoing.
An ongoing KC-led review into Sharp's appointment as BBC chairman is investigating whether he failed to properly disclose details of his involvement in the facilitation of an £800,000 loan guarantee for the then-prime minister Johnson. He has denied any involvement in the arrangement of a loan for Johnson.
Sunak said: "He was appointed before I was prime minister through an independent process. And that process is also now being reviewed independently.
"It's right that we let that review complete."
Lib Dem leader Sir Ed said the prime minister needed to sack Sharp, adding: "The BBC needs a proper independent chair not a Johnson acolyte".
Labour leader Sir Keir Starmer said Sharp's position was "increasingly untenable".
- BBC
