"This is a significant loan signing for the club," Rangers manager Jim Magilton told the club's website
"The fact we have been able to attract a player of Steven's calibre to the club speaks volumes of the board and the direction in which the club is heading.
"He's a class act, he can pass, tackle, shoot, he's box-to-box - a very, very good player."
Magilton swooped for Reid after serious injuries sidelined fellow midfielders Martin Rowlands and Gavin Mahon in recent weeks.
Rovers manager Sam Allardyce commented: "We had a chat and it was Steven's decision. He said he fancied it and wanted to get a few games under his belt to improve his fitness. Obviously we'll be seeing how he does."