The former England footballer was suspended on Friday after using Twitter last week to compare the language used to launch the new policy to the rhetoric of Nazi-era Germany.
His comments and removal sparked days of frenzied media coverage, that escalated on Friday after fellow presenters, pundits and commentators refused to work over the weekend in support.
That threw the publicly funded broadcaster’s sports coverage into disarray, curtailing its highlights package to just 20 minutes, without commentary or analysis.
But on Monday the two sides said they had come to an agreement that would see Lineker return to screens and the launch of an internal review into the corporation’s social media guidelines.
“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,” said BBC director-general Tim Davie.
In a joint statement, Lineker, 62, said: “I am glad that we have found a way forward. I support this review and look forward to getting back on air.”
He tweeted separately that the last few days, during which he has been mobbed outside by London home by reporters, photographers and camera crews, had been “surreal”.
But in a parting shot he added: “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.”
Davie apologised for the disruption to the service, saying he recognised the “potential confusion caused by the grey areas of the BBC’s social media guidance”.
“Impartiality is important to the BBC. That is a difficult balancing act to get right where people are subject to different contracts and on air positions, and with different audience and social media profiles,” he said.
The independent review will look at how the guidance applies to staff and freelancers such as Lineker, he added.
Former Leicester, Everton, Tottenham and Barcelona striker Lineker, who has hosted refugees in his home, has been an at times outspoken figure against government policy, particularly on immigration.
His comments overshadowed the announcement of plans to toughen laws governing asylum seekers, including the removal of those coming to the UK across the Channel from northern France in small boats.
The proposals were widely condemned by rights groups and the UN refugee agency, whose high commissioner Filippo Grandi on Monday sub-tweeted the UK government in his response to Sunday’s Oscars.
“Small boats carry big talent,” he wrote of the best supporting actor award for Ke Huy Quan, who fled Vietnam for a refugee camp in Hong Kong before moving to the United States.
Critics of Lineker said he should stay out of politics, given his high-profile sports presenting position, and Davie’s drive for BBC impartiality.
The BBC has also come under repeated criticism in recent years from politicians of all stripes, for perceived bias in news reporting, particularly over the UK’s divisive departure from the European Union.
But Lineker has argued that as a freelancer not working in news he is not bound by the same social media rules, while his supporters point to other potential conflicts of interest in the BBC.
Notably they have highlighted the role of the BBC chairman Richard Sharp, a donor to the ruling Conservative party who facilitated a loan to former prime minister Boris Johnson.
They also questioned Davie’s own past links to the Tory party, and the presence on the BBC board of Robbie Gibb, who was a former Downing Street communications director in Theresa May’s government.