A date of departure has not yet been finalised but he is expected to take up his new position at the full-service agency in the New Year.
A spokesman for TBWA\London confirmed the move and said the agency's search for Hunter's replacement is well underway.
Robert Harwood Matthews, president of TBWA\UK, said: "Professionally it's very flattering that Deutsch rate our work so highly.
"We're already in the advanced stages of finding a new executive creative director at TBWA\London, which will complete the reenergised exec team. I’d like to thank Mark for his work over the past year."
Hunter joined TBWA\London in April 2009 after leaving Euro RSCG London following a management restructure.
At Deutsch LA he replaces Eric Hirschberg who left the agency in July for the role of chief executive at Activision Publishing.
Before joining Euro RSCG London in 2007, Hunter worked at Wieden & Kennedy Amsterdam and Bartle Bogle Hegarty.
In September TBWA overhauled its management team with the appointments of Isobar managing director, Andy De Groose, as its new managing director, and the Saint@RKCR/Y&R managing partner, Zaid Al-Zaidy, as its chief strategy officer.
Al-Zaidy replaced Tom Morton, who left in July to join Publicis as its chief strategy officer.
De Groose was effectively a replacement for Matt Shepherd-Smith, who quit as TBWA\London’s chief executive in December last year.