The lock, who made six appearances during the tour of South Africa including all three Tests, has been linked with a move to the Top 14 with Clermont Auvergne leading the chase.
But he has signed a new three year deal at the Ospreys.
"It's my home region and I'm proud to represent the Ospreys," said Jones. "I'm thankful to the coaches and the directors for having faith in me and for allowing me the opportunity to continue with the region."
There had been fears of a mass exodus from the Swansea-based region after fellow Lions James Hook and Lee Byrne announced moves to the Top 14 next season - with Perpignan and Clermont Auvergne respectively.
2005 Lion Gavin Henson also walked out last October, while 2009 tourist Mike Phillips could be released from his bumper contract.
But the Ospreys skipper has refused to follow his fellow Lions lead and insists the region have a bright future.
"I know that I'm fortunate enough to wear the Ospreys shirt but I'm a fan first and foremost," added Jones.
"It would have been a far more difficult decision to move on than it has been to stay.
"I've never wanted to play anywhere else and I've never said otherwise. It's flattering to have interest from France and offers from other clubs, but I'm very conscious that the grass isn't always greener on the other side."