The move brings an end to a crisis for the network that had begun when the sports presenter was suspended because of a Twitter post about British immigration policy.
The British public broadcaster’s suspension of one of its highest-profile anchors has become a sprawling conflict that poses risks to its reputation for neutrality and independence.
Mr. Lineker, one of England’s best-known sports personalities, had criticized his government’s policy on social media. His ouster led to an implosion of the soccer program “Match of the Day.”