The 21-year-old, who has captained the region and Wales at age-grade level, has put pen to paper on a two-year deal which will keep him at the Liberty Stadium until the summer of 2015.
Peers made his debut in the LV= Cup defeat at Exeter last season, and has performed well after being thrust into the first team in the wake of injuries to the first-choice lock pairing of Alun Wyn Jones and Ian Evans.
Peers, who trained with the national squad during the recent autumn Tests, said: "I'm really excited about signing this contract. The Ospreys are my home region and I've come through the age grade system here so this is the next big step for me.
"In my position, where there are quality international players ahead of me, I'm definitely learning from the best, people who have been there and done it for the Ospreys and for Wales.
"It's a great place for me to learn my trade in the second row."