Diallo has made just nine first team appearances for the Red Devils since joining from Atalanta for £37m in January last year.
The 19-year-old Ivory Coast international has been restricted to a solitary appearance this season after picking up injury at the start of the campaign.
Diallo has expressed delight at the temporary switch and could make his debut for Rangers against Ross County this weekend.
Diallo told the Rangers official website: 'It is fantastic for me at this stage of my career to have the opportunity to come to such a big club that is challenging on a number of fronts and will give me some excellent opportunities to test myself in many environments.
'I look forward to training with my teammates for the first-time tomorrow and to meeting the fans for the first time at Ross County on Saturday.'
Rangers manager Giovanni Van Bronckhorst added: 'He is a player who I have been aware of for some time, and when the opportunity to sign him came up, we very keen to make it happen.
'He will add a lot to our squad and provide even more competition for the players in the forward areas.'
Rangers are four points clear of Celtic in the race for the Scottish Premiership title.
