It means the WPP media agency group is losing the head of its biggest market while in the middle of a wide-ranging restructure.
Lesser had only been appointed as North America chief executive in 2015, replacing Kelly Clark, who is now global chief executive.
Clark is overseeing a global merger of Group M agencies Maxus and MEC and trying to turn digital agency Essence into a fourth global media network.
Group M will now begin a search for Lesser's replacement, with Clark assuming Lesser’s responsibilities in the short-term.
Prior to joining Group M, Lesser was a key figure in WPP’s transition to programmatic media trading, and helped to build and run Xaxis, Group M’s programmatic buying-arm.
At AT&T, Lesser will be chief executive of a new business unit that will build an advertising and analytics platform for the data and content assets AT&T will acquire from its pending deal with Time Warner.
MEC lost AT&T to Omnicom's Hearts & Science in a major blow a year ago and the account loss is widely thought to have been a factor behind Group M's subsequent decision to merge the agency with Maxus.
A Group M spokesman said: "Brian has been a key contributor to 24/7, Xaxis and most recently Group M, and we are sorry to see him go, but wish him every success in his new role. We will immediately start the search for a replacement."