The award is given annually to an athlete or athletes who best personify athletic achievement and sportsmanship on and off the field.
"It's much more than just two people," Watt said. "It's a whole city. On my side, it's over 200,000 people who donated money to help rebuild the city. It's an award that's so much bigger than sports."
After Hurricane Harvey hit Houston in August, Watt started a fundraiser to help those affected by the devastating flooding in the area. In less than three weeks, Watt raised more than $37 million.
In October, Watt announced that $30.15 million of the funds will be distributed among four nonprofit organizations to help rebuild homes, restore child care centers and provide food and medical care.
Watt has been on injured reserve since Week 5, after he broke his leg against the Kansas City Chiefs. Watt was in New York City on Monday, and he appeared on "The Tonight Show Starring Jimmy Fallon" when the award was announced.
Watt discussed his injury, saying he is feeling great while recovering from his surgery. He had a cane while he was on the show but joked that he just uses it to "one, appease my trainer, and two, to get sympathy from my girlfriend."
Watt also talked to The Associated Press on Monday, saying he's confident he'll return for the Texans next season.
Watt began walking without the help of crutches last week, and he is looking forward to the next steps in his rehabilitation.
"It's a long process,'' he told the AP. "So it's walking, it's strengthening, then eventually it's running and getting back to football. But we're on track, and next season shouldn't be a problem, I don't believe. I have a very excited attitude, and we obviously have great rehab guys and trainers and stuff, so it's going to be good.''
Watt knows that he has a long way to go before he'll be ready to play football again, but the 28-year-old defensive end got a boost when he was able to walk again.
"Friday was my first day walking, and it was an extremely happy day,'' Watt said. "You don't get to walk for two months, it's crazy how such a simple thing like walking can really just -- it was awesome. So now to be able to move around, I feel great. I feel really good. I'm very excited about the rehab process. Obviously, it's a long process, but I'm excited.''
Information from The Associated Press was used in this report.