Davis set a British record for male international caps with 140 appearances for Northern Ireland.
He had two spells with Rangers, playing a central role in four Scottish Premiership titles, as well as lifting the Scottish Cup and Scottish League Cup on three occasions.
He had a spell as caretaker manager at Rangers earlier this season following the departure of Michael Beale, while rehabilitating from a long-term knee injury sustained in December 2022.
Davis, who helped Rangers finish as Europa League runners-up in 2008 and 2022, was named an MBE in 2017 for services to football.
He played for Aston Villa and Fulham prior to his initial move to Ibrox, leaving Scotland in 2012 to spend seven years with Southampton before returning to Rangers.
"It's a strange sensation today, but ultimately it has been at the back of my mind given the nature of the injury and my age," Davis said.
"I did some testing four weeks ago and I realised I was still a little bit away. It feels like the time is right and I'm comfortable with it.
"It's been an incredible journey to get to two European finals and win the trophies that I have, share those moments with the fans, be within the dressing room with your family after the games.
"It's such a special football club and it goes without saying that I'm going to miss it, but I've had an incredible time here."
