The former Sunderland winger has retuned to the Championship in the pursuit of more playing time.
His minutes have been very limited with the Seagulls but he is seen a bright longer-term prospect.
Millwall are in the thick of the promotion race and look well placed for a play-off spot.
Head coach Fabian Hurzeler said: “Tommy has settled in well, but has had a frustrating time with injuries, but he’s now fit and keen to play, and this gives him the opportunity.
“He is an exciting young player, and he now has the chance to help Millwall with their Premier League promotion push.
“The move will really benefit his development. It will give him significant game time and allow him to build on an outstanding breakthrough season with Sunderland last season, where he was integral in their promotion.
“We wish him well for the second half of the season and look forward to welcoming him back in the summer.”
Albion could complete more outgoing loan business ahead of the 7pm deadline on Monday.
They confirmed a permanent move for under-21s midfielder Joe Knight to Stevenage this weekend.