The contract extension would take effect beginning with the 2008-09 season. The Pittsburgh Post-Gazette said the deal is worth $43 million.
Crosby, who turns 20 next month, won the Art Ross Trophy as the leading scorer in the NHL last season and also the Hart Trophy as regular-season most valuable player.
He scored 36 goals and had 84 assists. In his two NHL seasons he has 75 goals and 147 assists for 222 points over 160 games. He is the youngest player in NHL history to reach 200 points.
"I really enjoy playing and living in Pittsburgh and I want to be here for a long time," Crosby said in a statement Tuesday. "Individual honors and scoring championships are great, but my No. 1 goal is to win the Stanley Cup. I'd love to be a part of bringing the Cup back here to Pittsburgh."