The Ibrox club applied to construct the new building at their Murray Park training ground in Milngavie, East Dunbartonshire.
They said it was needed to create more room for young players as space was restricted at their current building.
The back of the new 216 metre square complex will include a stand for spectators to watch youth games held at Murray Park and new floodlights will also be erected.
The club submitted an application to East Dunbartonshire Council earlier this year and it has now been granted by planning officials.
In a letter to the council, the club’s architect Scott Hammond explained the need for the new building.
He said: “It will simply provide more space for changing; the existing accommodation is currently severely restricted.
“The facility will alleviate the club’s existing logistical problems but will not result in an increased volume of cars or spectators.
“It is intended to allow the club to manage capacity issues resulting in a significantly improved experience to develop their young players.
“The youth games are played predominantly on a Saturday and Sunday between 10.30am and 5.00pm. There are occasional midweek matches.
“The key point is that the introduction of the new facility will not increase the number of games already played and hence it is anticipated that the volume of traffic and spectators will remain the same as it has done for many years.”
In a written report, the local authority said: “Having taken account of all material considerations the proposal is considered to be acceptable.
“The proposal is compatible with its surrounds in terms of land use, design and scale and will not cause any unacceptable impact to the surrounding environment or closest properties.”
The £14 million training complex was opened in July, 2001, and was named after previous owner Sir David Murray.
It includes six full size pitches, two half size pitches, a practice area, a synthetic indoor pitch and the training centre housed within a 38 acre site.
Last year current Rangers chairman Dave King asked fans to submit suggestions for a new name for the training ground which he said was now referred to within the club as ‘Auchenhowie’ - the area of Milngavie in which it sits.