The veteran broadcaster is leaving the BBC after more than two decades, including 16 years at the helm of his own Sunday morning show.
Bringing his final programme to a close, he said: “That it is, all over, I have been so lucky and so privileged to share so many Sunday mornings with you.”
Referring to the catchphrase of the fictional news anchor played by Will Ferrell in the 2004 hit comedy, he added: “I have been wondering how to close this final show, but I can’t do better than quoting my great mentor: ‘You stay classy, San Diego.'”
His final programme featured a montage of highlights of the show over the years, including interviews with Tony Blair, Greta Thunberg, Barack Obama and Vladimir Putin.
Among his final guests were actor David Tennant and Health Secretary Sajid Javid, who both expressed regret at his departure.
Sophie Raworth will serve as the interim presenter of the Sunday morning programme, which will be temporarily retitled Sunday Morning, from January 9.
Marr, 62, has previously said he will now focus on writing and presenting political and cultural shows for Global, and writing for newspapers.
He said moving to the London-based media company offers him a “new freedom” to do “fast-paced, very regular political journalism on LBC with no filter”.
Marr joined the BBC in May 2000 as political editor.
He will host an opinion-led programme on LBC which will see him “give his view on the biggest issues of the moment” alongside guests, Global said.
He will also present a new programme on Classic FM, playing music and interviewing guests from the world of politics and arts, host a weekly podcast on Global Player and write a regular column for the LBC website.