The Coyotes say the deal is pending Langkow's passing a physical.
Langkow, a center, played for Phoenix from 2001 to 2004, scoring 68 goals with 98 assists in 243 games before being traded to Calgary. The 34-year-old played just four games with the Flames last season because of a lingering neck injury from the previous season.
The fifth overall pick by Tampa Bay in the 1995 NHL draft, Langkow has 259 goals and 383 assists in a career that included a stop in Philadelphia.
Stempniak had 19 goals and 19 assists while playing all 82 games with the Coyotes last season.
Both players are set to become unrestricted free agents at the end of the coming season. Stempniak will make $2.3 million with a cap hit of $1.9 million this season while Langkow will make $4.5 million in the final year of his deal.
Scott Burnside covers the NHL for ESPN.com. Information from The Associated Press was used in this report.