Amad has made just one appearance this season, coming against Young Boys in the Champions League
The deal, which was completed on Thursday, will see the forward turn out for Rangers for the rest of the season, before returning to United for the start of pre-season.
There is no option for the Scottish champions to make the switch permanent and Red Devil bosses still have extremely high hopes for his development.
And Rangers Sporting Director Ross Wilson confirmed that United pored over potential options, before sanctioning the move to Glasgow.
“This is a really exciting signing for us as Amad was highly sought after by a number of clubs,” Wilson explained.
"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.
“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.”
Meanwhile, Amad himself has admitted that now is time for him to continue his development and to challenge himself out of the comfort zone of Carrington.
Hopes are high for Amad, who signed for Man Utd in a deal that could reach £37m
“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,” he told the club’s official media team.
“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.”
United bosses will have a keen eye on proceedings at Victoria Park on Saturday lunchtime, as a player they have earmarked as a star of the future hopes to make an immediate impact.