The Yorkshireman, 28, is the first European winner at Augusta since 1999 and only the fourth British champion.
"It's a great feeling and hopefully one we can have many more times," said Willett of his first major victory.
Willett's manager Chubby Chandler said the golfer could win another major this year and become number one in the world "without any doubt".
Carding a final-round five-under-par 67, the Englishman took advantage of defending champion Jordan Spieth dropping six shots in three holes.
The last European to win at Augusta was Spaniard Jose Maria Olazabal, while the only other British champions have been Nick Faldo (1989, 1990, 1996), Sandy Lyle (1988) and Ian Woosnam (1991).
Chandler said Willett, a 2007 Walker Cup team-mate of three-time major winner Rory McIlroy, could "become one of the greats of his time".
