The contract is for one year; CapGeek.com lists it at $900,000. The Rangers have about $12 million in salary cap space to sign restricted free agent forwards Derick Brassard, Mats Zuccarello, and Chris Kreider, and defenseman John Moore.
Stempniak, a 31-year-old right wing, has 637 games of NHL experience. He has scored 150 goals and assisted on 191 others for 341 career points.
After playing 52 games for the Calgary Flames last year, Stempniak was sent to the Penguins before the trade deadline in exchange for a third-round pick in the 2014 draft. He posted 11 points to close out the regular season before notching two goals and an assists in 13 playoff contests.
Stempniak was part of a Pens team that was eliminated by the Rangers after holding a 3-1 series lead in the second round.
A fifth-round pick by the Blues in the 2003, Stempniak began his NHL career in St. Louis and has also made stops in Toronto and Phoenix.