Kane finished first in the Hart Trophy voting with 1,395 voting points and 121 of the 150 first-place votes available. Pittsburgh Penguins center Sidney Crosby was first runner-up with 800 points and 11 first-place votes. Jamie Benn of the Dallas Stars was third.
Benn and Washington Capitals goalie Braden Holtby were the other finalists for the Ted Lindsay Award.
Video: Patrick Kane is presented the Ted Lindsay Award
With 106 points in the regular season, Kane was already the first American-born player to win the Art Ross Trophy as the League's leading scorer. He scored 40 of those points during a 26-game point-scoring streak, a record for players born in the United States.
"It's amazing to me that there's no American that's ever won the scoring title or the MVP award because there's been so many great American players," Kane said. "You can go up and down the list of names, guys like [Chris] Chelios, Brian Leetch, Mike Modano, Joe Mullen, Jeremy Roenick -- players that have had great careers. I don't know if I was lucky or fortunate to be in that position, but it's pretty amazing to say some American records you hold now, whether it's the MVP, scoring title, point streak. It's pretty exciting."
Crosby said he wasn't surprised Kane won the Hart Trophy.
"Just being in the conversation was nice, but I was kind of expecting [Kane] to get it," Crosby said.
Kane helped Blackhawks rookie left wing Artemi Panarin score 77 points in 80 games, good enough for the latter to win the Calder Trophy as the League's top rookie.
Panarin, who played on a line with Kane and center Artem Anisimov, finished with 1,258 voting points and 88 first-place votes. Philadelphia Flyers defenseman Shayne Gostisbehere and Edmonton Oilers center Connor McDavid were the other finalists.
"Without Patrick Kane, I may not have gotten this award," Panarin said through a translator.
Kane said he feels the same way about Panarin.
"There's no doubt in my mind he's a huge reason for my success," Kane said. "I'll take it one step further and say Anisimov was a huge part of that as well. It was a lot of fun for our first year together and hopefully we're together for a long time."
Video: Braden Holtby is awarded the Vezina Trophy
Holtby didn't leave empty-handed; he took home the Vezina Trophy as the League's best goalie, beating out Ben Bishop of the Tampa Bay Lightning and Jonathan Quick of the Los Angeles Kings.
Holtby, who was first on 26 of the 30 ballots submitted by NHL general managers, finished with 48 wins, tying Martin Brodeur's NHL record for most in a season. He had a 2.20 goals-against average and .922 save percentage.
"I still think I can get a lot better," Holtby said.
Capitals coach Barry Trotz won the Jack Adams Award for the first time in his career. This was the third time he was a finalist.
The Capitals won the Presidents' Trophy with 120 points. They set a franchise record for total wins (49) and road wins (29).
"I thought we were a heavyweight this year," Trotz said.
It was a big night for the Kings; defenseman Drew Doughty won the Norris Trophy and center Anze Kopitar won the Selke Trophy and the Lady Byng Trophy.
Doughty was named on 147 of the 150 ballots submitted and received 93 first-place votes and 1,254 voting points. He is the second player in Kings history to win the Norris Trophy as the League's top defenseman (Rob Blake in 1998).
Doughty had 51 points, averaged 28:01 of ice time per game and helped the Kings finish third in goals-against per game (2.34). He had a plus-24 rating and a 58.89 shot-attempts percentage (SAT). He was on the ice for 537 more even-strength shot attempts than against.
"I've been so close twice, and to kind of get a sniff at it but not finishing the deal kind of [stunk]," Doughty said. "But it feels great just to win that award after the history of it, Nick Lidstrom winning it, guys like that that I looked up to as a young kid. Yeah, it's really special to me."
Video: Drew Doughty is presented the Norris Trophy
Kopitar is the first Kings player in history to win the Selke Trophy as the League's top defensive forward. He finished second in the voting in 2014 and third last year. He is the first Kings' player to win the Lady Byng Trophy, awarded to "the player who best exhibits sportsmanship and gentlemanly conduct combined with a high standard of playing ability," since Wayne Gretzky in 1994.
Kopitar led the Kings with 74 points and had 16 penalty minutes despite leading all NHL forwards in total ice time (1,690:12). He was second in the NHL with a plus-34 rating and third among forwards in SAT (57.5 percent).
Ten days after his team won the Stanley Cup, Pittsburgh Penguins general manager Jim Rutherford won the General Manager of the Year Award.
Rutherford was first on 10 of the 40 ballots submitted by the League's GMs and a panel of other NHL executives, along with print and broadcast media members. The vote was conducted after the second round of the Stanley Cup Playoffs.
"We got the big prize and that was really the one we were looking for, but any time a team gets recognition with another award it's an honor," Rutherford said. "I view this really as a team award. It takes everybody involved in it. It takes all cylinders going. We're very fortunate."
Panthers right wing Jaromir Jagr won the Bill Masterton Trophy for his sportsmanship as well as his dedication and perseverance to the game. Jagr, 44, led the Panthers with 66 points and helped them set franchise records with 47 wins and 103 points.
In addition, Nashville Predators captain Shea Weber won the Mark Messier NHL Leadership Award, Vancouver Canucks captain Henrik Sedin won the King Clancy Memorial Trophy, and Calgary Flames captain Mark Giordano won the NHL Foundation Player Award.
Complete list of 2015-16 NHL Award Winners:
Hart Trophy: Patrick Kane, Chicago Blackhawks
Norris Trophy: Drew Doughty, Los Angeles Kings
Vezina Trophy: Braden Holtby, Washington Capitals
Calder Trophy: Artemi Panarin, Chicago Blackhawks
Ted Lindsay Award: Patrick Kane, Chicago Blackhawks
Selke Trophy: Anze Kopitar, Los Angeles Kings
Lady Byng Trophy: Anze Kopitar, Los Angeles Kings
King Clancy Trophy: Henrik Sedin, Vancouver Canucks
Jack Adams Award: Barry Trotz, Washington Capitals
General Manager of the Year award: Jim Rutherford, Pittsburgh Penguins
Masterton Trophy: Jaromir Jagr, Florida Panthers
Messier Leadership Award: Shea Weber, Nashville Predators
NHL Foundation Player Award: Mark Giordano, Calgary Flames
EA SPORTS NHL 17 cover vote: Vladimir Tarasenko, St. Louis Blues