Martin signed a new three-year deal yesterday.
"Having just been appointed as manager I'm delighted that one of my first actions is to offer Russ this new three-year deal," Hughton said.
"He's had a fantastic couple of seasons here since joining the club in January 2010 and this new deal shows what's he's done for the club over that time.
"He's been an ever-present and has shown he's a versatile player playing at both right-back and in the centre last season.
"Russ deserves this new contract and I'm delighted that he will be here for the next three years."