The team made the announcement official at a luncheon Thursday.
"Sidney has done so much for this franchise in his first two seasons, made so much history, that you have to keep reminding yourself that he is only 19 years old," Penguins general manager Ray Shero said in a statement.
"But Sid's contributions extend far beyond statistics and his incredible achievements on the ice. It is obvious to all of us - coaches, players, management, staff - that he has grown into the acknowledged leader of the Pittsburgh Penguins.
"It is only appropriate that he wears the C as team captain."
Crosby, who won't turn 20 until August, led the league in scoring with 120 points (36 goals, 84 assists) in his second season with the team. The team followed Crosby to its first playoff berth since 2001, losing in the first round to the Ottawa Senators.
Crosby, a native of Cole Harbour, N.S., is the youngest NHL captain by about two months. The Tampa Bay Lightning named Vincent Lecavalier captain in 2000, when he was 19 years 11 months old, but later took the title from him.
The Penguins have not had a captain since Mario Lemieux announced his retirement in January of last year.
"I don't think it will be that much different than last year. The C adds a little bit, but it's just a letter," defenceman Ryan Whitney told the Pittsburgh Tribune-Review. "He's been a leader and will continue to be. This shows the rest of the league that he has completely arrived."