Paisley-born Neil will be replaced by a fellow Scot - BBC Scotland Editor Sarah Smith, who will continue in her current role which is based at the Corporation’s HQ in Glasgow.
Mr Neil is best known as the face of the Daily Politics, which covers the day’s big political news and has regular dispatches from parliament including Prime Minister’s Questions.
He also hosts the more off-beat political magazine show This Week, which airs after Question Time every Thursday and is famous for its quirky VTs which often feature political journalists in fancy dress.
The former Scotsman executive will continue to host those two shows, and will presumably take more time to focus on his outside interests which include being Chairman of the company which publishes the Spectator magazine.
His salary was revealed in the publication of BBC pay to be between £200,000 and £249,000 a year, which some considered relatively small in comparison to some of his colleagues.
Ms Smith, who is the daughter of the late Labour leader John Smith, was appointed BBC Scotland Editor in 2015 after previously working for Channel 4 and presenting Newsnight Scotland replacement “Scotland 2014” in the run-up to the Independence Referendum in 2014.
Ms Smith told the BBC: “Andrew is one of the great political interviewers who leaves big shoes to fill. I am thrilled to take on this role at such an exciting time in British politics.
“I am very much looking forward to working with the Sunday Politics team.”
Mr Neil added: “I loved presenting Sunday Politics, it was a privilege and honour to hold the political discourse up to the light for all those years and while I will miss it greatly I am delighted to continue to work for the BBC on other projects. I wish Sarah the best of luck with this challenging and wonderful production.”