The winner will be announced during the Stanley Cup final. Each GM is a finalist for the first time.
In his first season as an NHL GM, Bergevin guided the Canadiens to a Northeast Division title. Montreal was also the league's most improved club this past season.
The Canadiens were second in the Eastern Conference standings after finishing 28th in the overall standings a year earlier. Bergevin hired Michel Therrien as head coach and selected centre Alex Galchenyuk with the third overall selection in the 2012 NHL Draft.
Murray oversaw a Ducks club that enjoyed its finest regular season in franchise history, capturing the Pacific Division and No. 2 seed in the Western Conference.
He strengthened Anaheim's goaltending by signing Sweden native Viktor Fasth as a free agent last May. Murray also bolstered the defence corps with the signings of Sheldon Souray and Bryan Allen and a trade for Ben Lovejoy.
Shero made key additions to an already-strong roster throughout the year that helped propel the Penguins to their first Atlantic Division title since 2008 and the No. 1 seed in the Eastern Conference.
He obtained centre Brandon Sutter and goaltender Tomas Vokoun in off-season trades and later brought defenceman Douglas Murray and forwards Jarome Iginla, Brenden Morrow and Jussi Jokinen to Pittsburgh in deals leading up to the trade deadline.
Voting for the award was conducted among the 30 club general managers and a panel of NHL executives, print and broadcast media.