Hart was promoted to the role in March 2013 after having previously been the general manager of advertising and online in the UK for two years.
Before Microsoft, Hart was the managing director of Associated Northcliffe Digital, where he had run the newspaper group's digital operations for six years.
A Microsoft spokeswoman told Campaign: "Andy Hart (VP, advertising and online, Microsoft Europe) has decided his next challenge lies outside Microsoft. We thank him for his contribution and wish him well for the future."
Meanwhile Stuart Flint, the UK sales director at Microsoft advertising and online, has today transitioned to AOL, along with the wider Microsoft ad sales team in the UK.
He retains his job title and will report into Hamish Nicklin, the managing director of AOL UK, who joined from Google two months ago.
Flint joined Microsoft in 2014 from Yahoo, where he briefly led the company in the UK as managing director following the exit of the previous managing director, James Wildman.
AOL, which is now owned by Verizon, will sell display, video and mobile ads for Microsoft in its nine key markets across the world and use the tech giant’s leading brands, including the MSN homepage, Outlook, Xbox and Skype.
An AOL spokesman said: "AOL and Microsoft have expanded their global strategic partnership to create more opportunities and greater scale for advertisers. Today, we will be welcoming new colleagues from Microsoft to AOL in the UK, Spain and Japan.
"Bringing with them a range of skills to complement our own, they will join us in our ambition to make us a ‘must buy’ for advertisers. AOL and Microsoft have a long history of working together and we are wholly committed to building a long-term and collaborative relationship."