21-year-old hooker Breeze has signed on for two years, while former Cardiff Blues wing Vaughton has followed New Zealand international Marty Holah in agreeing a one-year extension to his current deal.
"The development of the best local talent is at the heart of everything we do here at the Ospreys, so it is always excellent news when we are able to retain the service of three local players who learnt the game at clubs across the region," said Ospreys coach Sean Holley.
"Steve Tandy was one of the first ever Ospreys and we are delighted to retain his services... he is a natural leader who is respected by his peers.
"Jonathan is now approaching 50 appearances for the region and is an important part of the current Ospreys squad. We believe that he can still improve further over the course of his new contract and look forward to helping him reach new levels.
"Marc Breeze has been a consistent performer for Aberavon RFC in the Welsh Premiership this season. After introducing him as a squad member this summer we have been impressed with his professionalism and his attitude to improve."