The comedian is leaving to focus on making his Slacktivist Action Group podcast and his new standup show, and has called for a female to replace him on the BBC Two comedy panel show.
"I'd like to thank all of the people I've worked with over the years on Mock and from the BBC," he said in a statement.
"However, when 'Unlikely Things to Hear in a Superhero Movie' comes around for the 4th time it is probably time to move on.
"Perhaps this will be an opportunity to make a female comedian a regular."
Speaking of his new ventures, he continued: "I, myself, am looking forward to chairing the new monthly show and podcast Slacktivist Action Group and delving a little deeper into the bigger issues affecting the UK.
"With what seems like an exciting time for politics in this country, this is something I'd like to focus more of my time upon, with a chance to host a show and set my own agenda.
"I would also like to take this opportunity to wish the BBC well in its fight to avoid even more damaging cuts - love it or lose it."
Andy has appeared as a team captain on ‘Mock The Week’ since taking over from Rory Bremner in 2007.
News of his departure follows Stephen Fry’s exit from BBC Two’s other hit panel show ‘QI’ last week, who has since been replaced by Sandi Toksvig.