The footballer-turned-broadcaster, 62, was taken off air for a tweet comparing the language used to launch a new Government asylum seeker policy with 1930s Germany.
But after he was begged to return, his first assignment back on the BBC would be to present live coverage of the FA Cup quarter-final between Manchester City and Burnley on Saturday, Mail Online reports.
Mr Lineker said today, “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. Thank you.”
The BBC director-general Tim Davie said in a statement the corporation would now commission an independent review of its social media guidelines, particularly for freelancers.
Minutes after the official BBC statement was published, Lineker tweeted, “After a surreal few days, I’m delighted that we have navigated a way through this.
“I want to thank you all for the incredible support, particularly my colleagues at the BBC Sport, for the remarkable show of solidarity. Football is a team game but their backing was overwhelming.
“I have been presenting sport on the BBC for almost three decades and am immeasurably proud to work with the best and fairest broadcaster in the world. I cannot wait to get back in the MOTD chair on Saturday.”
In a follow-up tweet, Gary Lineker said he wanted “to thank Tim Davie for his understanding during this difficult period.”
He added, “He has an almost impossible job keeping everybody happy, particularly in the area of impartiality. I am delighted that we’ll continue to fight the good fight, together.”
Confirming Lineker would return to Match of the Day on Saturday, Mr Davie said the presenter “will abide by the editorial guidelines” until a review of the BBC’s social media policy is complete.
In his statement issued on Monday, the director-general said, “Everyone recognises this has been a difficult period for staff, contributors, presenters and, most importantly, our audiences. I apologise for this.
“The potential confusion caused by the grey areas of the BBC’s social media guidance that was introduced in 2020 is recognised. I want to get matters resolved and our sport content back on air.”
Mr Davie told the BBC he did “the right thing” in asking Lineker to step back from presenting duties, but said he “respects the views” of the presenters and pundits who walked out in solidarity with the former England striker.
According to Mail Online, the BBC Board said it welcomed the agreement between Lineker and the broadcaster, saying it was “the right time” to review its social media guidelines.
A Downing Street spokesman declined to say whether the Prime Minister had confidence in Tim Davie following the impartiality row, stressing that the choice of BBC director-general was a matter for the corporation.
Asked about the PM’s position on the licence fee, the spokesman said, “We remain committed to the licence fee for the rest of the current charter.
“But we’ve been clear that the BBC’s funding model faces major challenges due to changes in the way people consume media and it’s necessary to look at ways to ensure long-term sustainability.”