In a statement released Thursday, owner George Shinn said the move gives the Hornets the best opportunity "to reach our goals this season."
The Hornets also announced that former New Orleans head coach Tim Floyd, who Scott replaced, will be one of Bower's top assistants.
New Orleans lost 124-104 at Phoenix on Wednesday, falling to 3-6 to start the season.
When Scott took over as coach following the 2003-04 season, he was the Hornets' third coach in three seasons. He was the NBA coach of the year in 2008, when Chris Paul led the Hornets to a 56-26 record.