Miguel Herrera has been fired as Mexico coach following allegations that he punched a television reporter.
Former Arsenal midfielder Abou Diaby has rejected an offer to join West Brom in favour of finding a new club in France.
Hegarty's current contract was set to expire in the summer and the 20-year-old has put pen to paper on a two-year extension.
Hegarty follows in the footsteps of youngsters Robbie Crawford, Barrie McKay and Lewis Macleod in extending their stays at Ibrox.
Manager Ally McCoist said: "All the boys deserve a lot of credit for coming through and doing their best to make an impact on the team.
"Chris Hegarty has been one of those lads who has come in and been really, really solid and we can look at him and see just how much it means to him to pull on that blue jersey.
"In this day and age that's really important especially in our current climate so he deserves the extension to his contract.
"These lads deserve the reward for their efforts and hopefully they'll be the future of the club for years to come."
Talks have also began with Kal Naismith and Fraser Aird in the hope of the duo also pledging their commitment.