Levet birdied the third extra hole to win for the first time since the 1998 Cannes Open.
Levet carded a final-round 3-under-par 69 to tie Swedes Mathias Gronberg and Robert Karlsson, and Englands David Howell at 14-under-par at the end of regulation.
Thomas Levet comments on his British Masters win
The biggest playoff on the European Tour since the 1993 Honda Open saw both Howell and Karlsson drop out on the first hole of sudden death after making a pair of bogeys.
Howell led Karlsson by one shot entering the final round.
The Frenchman had a chance to end the tournament on the 73rd hole, but pulled his four-foot birdie putt.
However, Levet redeemed himself by sinking a five-footer on the second extra hole to extend the playoff.
On the third hole of sudden death, the 176-yard par-3 17th, Levet stuck a 6-iron to 10 feet. He then made the putt and circled the green giving high-fives to the crowd. The scene was similar to that of the one provided by Hale Irwin after winning the 1990 U.S. Open.
Yes, magnifique is the word, said Levet. It is unbelievable to win in such a big tournament. Ive won many times in France, but every time outside France I seem to finish second or whatever, so this is unbelievable.
With the victory, Levet moves to 63rd on the Volvo Order of Merit. He also climbs to 13th on the Ryder Cup standings.
The last Frenchman to win in England was Arnaud Massy in the Open Championship at Royal Liverpool in 1907.
Full-field scores from the British Masters