The Indianapolis Star also reported team President Larry Bird will likely take a year off for unspecified health reasons before deciding his next career move.
Morway had been the Pacers' vice president of basketball operations since 1999 and added the title of general manager in 2008.
Indiana is coming off a 42-24 regular-season record. The Pacers made it to the Eastern Conference semifinals in post-season play.
"I've had a terrific 13-plus years with the franchise," Morway said. "The performance of this year's team both on and off the court was incredibly rewarding. To experience Bankers Life Fieldhouse full to the rafters again, with an energy reminiscent of the late '90s, and to see our fan base re-engaged and proud made it all worthwhile."