Bennett, 46, replaces John McKay, who resigned Oct. 8 as head coach and became the team's vice president at the end of the season. McKay was the only coach in the team's nine-year history.
Bennett compiled a 46-41 record with the Falcons in regular-season play between 1977 and 1982 and led Atlanta into the playoffs three times, compiling a 1-3 record in postseason games. The club's best finish during his tenure was a 12-4 record in 1980 when the Falcons won the NFC Western Division title.
"Leeman is a proven winner who brought about the greatest days in the history of the Atlanta Falcons," Tampa Bay owner Hugh Culverhouse said. "He comes highly recommended, and I have been very impressed with him in a series of interviews.
"He is highly organized and motivated . . . I have great confidence. He represents the best possible coaching choice for the Buccaneers at this time," Culverhouse said.
Bennett, who was en route to Tampa Wednesday afternoon, produced a playoff team in his second season with the Falcons but was fired after Atlanta was 5-4 during the strike-shortened 1982 season.
Culverhouse said that while Bennett had not signed a contract, the two had a "five-year understanding" that would afford the new coach time to put together the best available staff and install a new system.
"I'm impressed with him. He's a competitor and will not accept failure," said Culverhouse, who passed over Wayne Fontes, a longtime McKay assistant.
"Wayne was broken-hearted," Culverhouse said, citing Bennett's prior head coaching experience as the deciding factor. "Like a true winner, nobody likes to come out No. 2. It's too bad we couldn't hire two head coaches."
Fontes, who came to the Bucs along with McKay in 1976, was in Tempe, Ariz., on Wednesday representing Tampa Bay at a scouting combine.
McKay had a 44-88-1 record in his nine years as Bucs coach. The team was 6-10 in 1984 and 8-24 over the last two seasons.