Williams, who became the first player from the Raptors to win the award, received 78 of a possible 130 first-place votes.
Williams has enjoyed a lot of success this year after tearing his ACL in January 2013. The 28-year-old, who was traded to the Raptors from the Atlanta Hawks, averaged a career-high 15.5 points this season, along with 1.9 rebounds, 2.1 assists and 1.1 steals per game.
"I didn't think I was going to be the same player [after ACL tear]," Williams told reporters. "I knew I wasn't going to have the foot speed I once had, I knew I wasn't going to be able to jump as high. But it taught me to be smart and I worked on different parts of my game. Being able to evolve and change my game to win this award is very gratifying.
"[The award} is just a reminder than anything is possible if you say faithful to the grind and stay faithful to the things that put you into a position to be successful."
Raptors head coach Dwayne Casey believes that Williams deserved to win the award since he has the heart of a champion and a never-give-up attitude.
"I'm excited about Lou, a guy who comes back from an injury and works hard and is dedicated to getting his body right," Casey said. "Nobody knew what he was going to bring to the table … whether he was damaged goods or whatever. He's proved to everybody he's the old Lou Williams."