Rea, 21, made his senior Albion debut in August's League Cup tie against Southend, for whom he went on to play 16 games for on loan earlier this term.
The Republic of Ireland Under-21 player is available for Saturday's League Two game against Plymouth.
"Glen is somebody we've had on our radar," Luton boss Nathan Jones said.
He told the club website: "Obviously he's someone who I know very well having worked with him for the best part of two and a half years."
Rea and Jones were colleagues during the latter's spell as first-team coach at the Amex Stadium.
Luton Town have signed centre-back Glen Rea from Championship side Brighton & Hove Albion on loan until the end of the season.