"Our team will be built around a humble, unselfish, attitude and sacrifice. It's hard to find that in today's world," Schiano said. "But that's who we'll be."
The 45-year-old Schiano inherits a squad that allowed the most points in the NFL this season.
Schiano promised the Buccaneers would be physical on offense but would also "take shots down the field." He believes the team has a "young, talented core of players" and said he studied the team before he felt comfortable about taking the job.
"There's been several opportunities to go to places that were, quote unquote, bigger names or bigger programs," Schiano said. "And at times I listened. But when I tried to put myself there, it just didn't feel good.
"As I went through this process, and pictured myself being the coach of the Tampa Bay Buccaneers, I only felt one feeling that was negative and that was sadness of leaving my players (at Rutgers). Other than that it was tremendous excitement. That's how I knew this was the one."
Team co-chairman Joel Glazer said Schiano's hiring marks "a new chapter for the Tampa Bay Buccaneers," adding that the coach "has a vision for what he wants to do."
The Morris era ended with a 10-game losing streak, during which a porous defense allowed 31 of more points in seven of the team's last eight games and the offense sputtered, with Josh Freeman throwing a career-high 22 interceptions.
Schiano also said he was not intimidated by making the transition from college to the pros.
"I'm awfully glad this isn't my first head-coaching job," Schiano said. "It's easy to point at the college coaches who have made this jump (who have trouble). But the percentages of college coaches and pro coaches are the same. Everyone has trouble. It's a competitive league. That's what makes it fun."
The Associated Press contributed to this report.