The 20-year-old midfielder 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 today by returning to Murray Park after the American was given extra time off in his summer break to the home-based players.
Mitchell said: “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.
Twelve of the 13 players who reported on Thursday are now under contract with Salim Kerkar still to confirm his future.
Bedoya was given permission to delay his return until after a weekend wedding in the USA while fellow Americans Carlos Bocanegra and Maurice Edu have been given extra time off following their international commitments.
Ten players objected to the transfer of their contracts from Rangers to the new company with two of those joining new clubs at the weekend - Steven Whittaker going to Norwich and Kyle Lafferty moving to Swiss club Sion.
Ally McCoist’s confirmed squad also contains Kirk Broadfoot, Lee McCulloch, Lee Wallace, Kyle Hutton, Ross Perry, Kal Naismith, Darren Cole and Kane Hemmings plus goalkeepers Neil Alexander and Scott Gallacher.
McCoist’s training squad was today supplemented by young goalkeepers Blair Currie and Liam Kelly and fellow youth team players Barrie McKay and Robbie Crawford.