His move ends an association with JWT that began 27 years ago. His awards haul at the agency includes a Campaign gold and a Cannes silver.
Mawhinney's decision follows the exit of his copywriting partner, John Donnelly, who left at the start of the year to join Vallance Carruthers Coleman Priest but has since gone freelance.
Mawhinney said: "Burnett's merger with D'Arcy has caused it to take its eye off the ball. But things have settled down in the past few months and good things only happen with stability."
The switch reunites Mawhinney, 54, with Jim Thornton, the Burnett executive creative director, with whom he worked at JWT. A writing partner will be hired to work with him across a range of accounts.
Thornton said: "I need experienced people who are good with clients. I don't think we as an industry value Billy's kind of experience and talent highly enough."
Mawhinney joined JWT in 1978 and he remained there for two years before returning to his native Belfast.
He came back in 1982 to begin his long-running partnership with the writer Nick Welch on accounts including Persil, Kit Kat and Kellogg.