Arians retired as coach of the Arizona Cardinals after the 2017 season.
Arians will have a four-year deal with a fifth-year option, a source told Rapoport.
Arians had previously said he would only be interested in the Cleveland job, but later said he would listen to offers in Tampa due to his relationship with Jason Licht.
The 66-year-old has had several health issues over the years, including a bout with prostate and kidney cancer.
The Buccaneers fired Dirk Koetter, who had coached the team the past three seasons, hours after their season-ending loss to the Atlanta Falcons.
His reputation is one of a high-flying offensive guru, with a knack for getting the most out of quarterbacks like Andrew Luck, Peyton Manning, Ben Roethlisberger and Carson Palmer. Rapoport adds that former New York Jets head coach Todd Bowles is their top target for defensive coordinator.
Arians, who has worked as a coach in the National Football League in different capacities since, 1989, also served as the interim head coach of the Indianapolis Colts in 2012.
Tampa Bay has not officially announced any coaching moves at this time.