The extension is worth $27 million, a source told ESPN.com's Pierre Lebrun.
Bouwmeester, 29, still has a year left on his current five-year, $33.4 million deal signed with the Calgary Flames in 2009.
The Blues acquired Bouwmeester at the trade deadline in exchange for a first-round pick, minor-league defenseman Mark Cundari and Swiss League goaltender Reto Berra.
Bouwmeester joined Calgary in 2009 after being drafted third overall by the Florida Panthers in 2002. He has 71 goals and 229 assists in 10 seasons with the Flames and Panthers.