The highly-rated 19-year-old arrived from Serie A side Atalanta last January, signing for a fee of £18.7million that could reach £36.5m with add-ons.
Diallo made eight appearances last term and was set to join Dutch club Feyenoord on a season-long loan in August, only for a thigh injury to scupper that move.
The Ivorian has only played one first-team match for United since returning to fitness and has now joined reigning Scottish champions Rangers on loan.
“I am delighted to join Rangers until the end of the season,” Diallo said. “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 team-mates for the first time tomorrow and to meeting the fans for the first time at Ross County on Saturday.”
Rangers do not have the option to make the deal permanent, with sporting director Ross Wilson calling Diallo “a really exciting signing” for Rangers.
“We have been working hard with Manchester United and Amad’s agents throughout January to reach an agreement for Amad to become a Rangers player,” he said.
“We have stayed patient in our discussions as we know what Amad can bring to our group.
“Amad and Manchester United had an array of options this window across the Premier League and in Europe so needless to say, I’m absolutely delighted that we have been able to convince both Manchester United and Amad that Rangers is the perfect place for him to continue to showcase his undoubted and exciting talent.”
Rangers currently sit top of the Scottish Premiership, with Giovanni van Bronckhorst’s side boasting a four-point cushion over Celtic.
“I am really pleased to add Amad to our squad for the rest of the season,” the Gers boss said. “He is a player who I have been aware of for some time and when the opportunity to sign him came up, we were 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.”
Meanwhile, Rangers have sold midfielder Juninho Bacuna to Birmingham for an undisclosed fee.
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