The deal, announced Thursday, is worth $11.55 million, a source told ESPN.com.
One year remains on Kunitz's current deal, which will pay him $3.75 million this season. The extension begins in 2014 and runs through the 2016-17 season.
Malkin agreed to an eight-year extension earlier this month. Pittsburgh is also negotiating with defenseman Kris Letang and forwards Pascal Dupuis and Matt Cooke, both of whom will become free agents next month.
General manager Ray Shero said the contract will carry an annual salary cap hit of $3.85 million.