The Scottish winger has a contract with Aberdeen running out in the summer and had rejected the opportunity to extend his stay at Pittodrie beyond this season.
With Wright stalling on a new contract with the Dons, Scottish Premiership table-toppers Rangers reached a pre-contract agreement with the player last month.
Though the 23-year-old agreed to move to Ibrox on a free transfer in the summer, the Gers have been looking to take the winger to the club before the end of the winter transfer window.
Steven Gerrard’s side have finally struck a deal with league rivals Aberdeen to sign Wright now instead of taking him on a free transfer in the summer.
The winger is now expected to complete the transfer to Rangers and will be available for team selection for the rest of the season.
Rangers’ deal with Aberdeen has also seen Ross McCrorie being given permission to make his loan move to Derek McInnes’ side permanent.
McCrorie joined the Dons on a season-long loan in the previous transfer window, with the Reds agreeing to make the move permanent at the end of the 2020/21 season.
That agreement has now been brought forward and McCrorie will now become a permanent Aberdeen player.
