The award is given annually to the player judged to be the most valuable to his team. The winner will be announced during the Stanley Cup final.
Crosby and Ovechkin have previously won the award, while Tavares is a finalist for the first time.
Tavares ranked third in the NHL with 28 goals this past season and led his team with 47 points in 48 games to help the Islanders secure their first post-season berth in six years.
The 22-year-old native of Mississauga, Ont., also ranked in the top 10 in the league in even-strength goals (19), power-play goals (nine) and game-winning goals (five).
Crosby missed the final 12 games of the regular season due to injury, but still finished fourth in the league with 56 points and second with 41 assists. He had 17 multi-point games and a plus-26 rating to help the Penguins claim the top seed in the Eastern Conference.
The 25-year-old native of Cole Harbour, N.S., previously won the Hart Trophy in 2007 and was a finalist for the award in 2010.
Ovechkin became the first three-time winner of the Maurice (Rocket) Richard Trophy as the NHL's goal-scoring leader this season after scoring 32 goals in 48 games. He also finished third in the league in points (56), first in power-play goals (16), first in power-play points (27) and first in shots on goal (220).
The 27-year-old Moscow native led the Capitals to an 11-1-1 record in April and their fifth Southeast Division title in the last six years. He previously won the Hart Trophy in 2008 and 2009 and was a finalist in 2010.
Members of the Professional Hockey Writers' Association submitted ballots for the award at the end of the regular season. The top three vote-getters were designated as finalists.
Penguins forward Evgeni Malkin won the Hart Trophy last year.