He will have authority over January transfer deals and may look to reshape the squad for the second half of the season.
Murty, the club’s development squad coach, was appointed caretaker boss when Pedro Caixinha was sacked in October.
He has presided over nine Premiership matches, winning six and losing three.
His notable scalps include back to back victories over Aberdeen and an away win over Hibs at Easter Road. He also became the first Rangers manager of 2017 to put together a run of three successive league wins.
Set against that were defeats to Hamilton, Dundee and St Johnstone.
Rangers said in a statement: “The club’s directors believe Graeme has demonstrated he is capable of handling this task successfully and are confident the players will continue to respond to his leadership in a positive manner. With so much still at stake in the current season this decision was not taken lightly but now that Graeme has been given full control he can work towards the obvious targets with greater focus.
“It is important to concentrate on the remainder of this campaign – the Scottish Cup and maintaining a challenge at the top of the Scottish Premiership – and with Graeme now in charge until at least the end of the season, he and the players can tackle the challenges ahead with renewed confidence and belief.
“Graeme has already secured a number of positive results – notably against Aberdeen home and away and Hibernian, also away – in recent weeks and more results like those are required.
“It should be noted that Graeme will have the final say on which additions will be made during the January transfer window, which should be perfectly understandable given that he’ll be working longer term with the first-team squad. This will allow him to make important judgement calls.”
Murty said: “It is a genuine privilege for me to be made manager until the end of the season. It’s a huge honour to be asked to do so and I will continue to give everything I have to ensure we have a positive second half of the campaign. There is still so much to play for and we cannot let our fans down.
“They have been incredible. They have given me so much great support during my two spells in the dugout and I would like to thank everyone for their backing. I would also like to thank the Board for showing faith in me and I will work tirelessly with the players and coaching staff in order to improve our league position and be successful in the Scottish Cup.”
Rangers’ director of football Mark Allen added: “Graeme will have the final say in player recruitment in January and an input into the type of players required next summer.”
Murty is likely to add to his coaching team in the coming days.