The 21-year-old started at Abercrave RFC and made his debut for his home region in 2014, only to suffer an injury that kept him out of Ospreys action until the 2016/17 season.
"It's been great this year to get some game time in the Anglo Welsh and then through to the Pro12," Price said.
"Now I'm looking forward to next season and trying to kick on from there."
Sam Davies, Justin Tipuric, Dan Baker, Hanno Dirksen, Dan Lydiate (on a national dual contract), Joe Thomas and Brian Mujati have all signed new deals with the Welsh region for next season, while Wales backs Cory Allen and James Hook have been confirmed as additions to the squad for 2017/18.
Fly-half Luke Price has signed his first professional contract with the Ospreys.