Rafinha has lost his place in a star studded PSG midfield and has only made five appearances this season; his last outing for the club came in October.
The 28-year-old’s temporary switch to the Reale Arena marks a return to Spain, where he has previously starred for Barcelona and Celta Vigo on loan.
Rafinha joined PSG on a free transfer in the summer of 2020 from Barcelona and made 34 appearances across all competitions in his debut season, winning the Coupe de France.
This term, Rafinha has found opportunities hard to come by and he was not included in PSG’s UEFA Champions League squad for the group stages.
"I am very happy to have arrived at a great club like this," he said at a news conference on Tuesday.
"A few months ago my representatives told me about Real's interest, which I found exciting because of the great things going on here and the club's ambition.
"That's what attracted me to the club and now I'm very excited to link up with my team-mates.
"I feel good and have been preparing for this opportunity, knowing that it could come, whether at Paris or another club. Now it is a matter of adapting."
Rafinha, younger brother of Liverpool midfielder Thiago Alcantara, has two caps for the Brazil national team.
