Gibson guided Arizona to a worst-to-first finish in his first full season as a big league manager.
Milwaukee’s Ron Roenicke finished second and Tony La Russa of the World Series champion St. Louis Cardinals was third. Voting was completed after the regular season.
Maddon won for the second time. His Rays overcame a nine-game deficit in September to beat Boston for the AL wild card.
Jim Leyland of Detroit was second and Ron Washington of Texas was third.