Cummings joined Forest from Hibernian in the summer, but has struggled to establish himself and was left out of the squad on Saturday for Aitor Karanka’s first match in charge.
At the end of his loan spell, Rangers have the option to strike a permanent deal for the 22-year-old, who has scored four goals in 17 club appearances this term.
Cummings made his Scotland debut in a 1-0 defeat to Holland in November.
“I’m absolutely delighted to come to such a massive club,” Cummings told RangersTV.
“Once I knew they were interested, there was no question in my mind that I wanted to sign for them.”
Rangers look set to add Norwich’s Russell Martin on loan on Tuesday, but they have work to do to secure the signature of Kilmarnock winger Jordan Jones.
The 32-year-old Martin has not featured for Norwich since a 4-0 defeat to Millwall on August 26 and subsequently lost his place in the Scotland squad.
Kilmarnock manager Steve Clarke, however, has described Rangers’ bid for Jones as “nowhere near acceptable”.
Killie turned down a reported B£350,000 offer for the 23-year-old, who is under contract until the summer of 2019.
Clarke said: “There’s been a bid, nowhere near acceptable. I would be a little bit sad if I was the player, to be honest, that the bid was so low.
“It was an easy one for the club to turn down.”
Rangers also made an enquiry over Hamilton midfielder Greg Docherty last week after completing earlier loan deals for Sean Goss and Jamie Murphy.
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