Gosper is joining the Omnicom-owned agency from McCann Erickson New York, where he was hired as the general manager less than a year ago.
His new position will see him heading TBWA\Chiat\Day New York and several of its sister agencies. Gosper will report directly to Jean-Marie Dru, the president and chief executive of TBWA\Worldwide.
The appointment places a question-mark over the future of Mildenhall, the managing director of TBWA\London. Mildenhall had been in talks with Shona Seifert, the president of TBWA\Chiat\Day New York, about a position in the New York office (Campaign, last week). It is now unclear how Gosper's appointment, above Seifert, will affect Mildenhall's New York aspirations.
Gosper is due to take up his new role on 7 September, when the situation with Mildenhall will be clarified.
A spokesperson for TBWA\Worldwide said: "Discussions are still ongoing. Nothing has been decided."
The New York senior management shake-up will also see Tom Carroll, currently the president of the Americas, promoted to the position of vice-chairman.
He also reports into Dru and is tasked with taking charge of growing the business worldwide.
Dru said: "With Brett's appointment, with Tom in this global role and with Shona continuing the great job she has been doing, we are extremely well-placed to accelerate TBWA's growth in the US and worldwide."
Gosper said: "It has been a very difficult decision to leave a great agency like McCann. However, this is a fantastic opportunity to work again with Jean-Marie and play a significant role in TBWA's future."
Before joining McCann in 2003, Gosper was the chief executive of Euro RSCG Wnek Gosper in London. In the early 90s, he worked at BDDP, an agency that Dru co-founded. It was rolled into TBWA when its parent company, GGT, was acquired by Omnicom in 1998.