The move gives the Canadian team a boost as it seeks to win its first gold medal since 2007.
Crosby became available after the New York Rangers beat Pittsburgh in five games in their first-round playoff series.
He led the Penguins with 84 points (28 goals, 56 assists) in 77 games in the regular season.
He added two goals and two assists in five playoff games.
The Penguins forward has played 10 seasons in the NHL, scoring 302 goals and adding 551 assists in 627 games.
He won the Hart Trophy as the NHL's most valuable player in 2007 and 2014 and led the Penguins to the 2009 Stanley Cup title.
Crosby has represented Canada six other times over his career, most notably at the 2010 Vancouver Olympics.
Crosby served as team captain in Vancouver and scored the game-winning goal against the U.S. in the gold medal final.
He played for Canada at the 2006 world championship in Latvia. He had a tournament-high 16 points and Canada finished fourth.