The 20-year-old made two competitive appearances for Rangers before his contract expired at the end of the season.
The Northern Irishman was one of 13 players who turned up for the club's first day of pre-season training on Thursday.
Alejandro Bedoya joined their ranks on Monday by returning to Murray Park after the American was given extra time off in his summer break to the home-based players.
Mitchell told www.rangers.co.uk: "I'm over the moon to be signing on again with Rangers. I'm really buzzing about it. It has been a hard summer for me so I'm delighted to get everything sorted now so that I can concentrate on my football."
Mitchell, who made his debut in a 2-1 defeat by Dundee United in March, joins compatriot Chris Hegarty in signing a deal with the relaunched Ibrox club, who are still waiting to see which league they will be accepted into next season.
"Before we broke up for the summer, the manager said the club was wanting to keep me on and I was happy about that," he said.
"I came back on Thursday and after a bit of testing and some talks with my agent, it was good to get the contract signed. It's terrible what has happened to Rangers but it gives me a great opportunity to come through and show what I can do.
"I feel good. I've kept myself going over the summer, have played a bit of five-a-sides and done a few runs so I can't wait for the season to start now. No matter what league we are playing in, the boys are going to give it their all to win games and get us back to where we belong."
Twelve of the 13 players who reported on Thursday are now under contract with Salim Kerkar still to confirm his future.
