Morris led the Bucs to a 10-6 record this season and nearly into the playoffs. The seven-win improvement was the biggest one-year gain in team history.
The option is worth $2 million per season, and it includes incentives that could pay Morris as much as $7 million total during the next two seasons based on performance, according to the newspaper.
The move, as well as extending the contract of general manager Mark Dominik, had been expected.
Dominik said earlier this week that he considered Morris, 34, the NFL's Coach of the Year.
"When I talk to anyone publicly or privately, I think we have the coach of the year in the National Football League right here in the building, he was right here in front of you guys," Dominik said. "I think he's deserving of the award. I think he's earned it.
We put a lot on his plate this year, and he has absolutely handled it all. Certainly we're disappointed that we're not playing and preparing for the Philadelphia Eagles right now, but at the same point, we all see where this ship is headed. That's why we're so excited about the plan that we started with about two years ago and where it's gotten us today."