The 33-year-old, who has fallen down the pecking order at the Britannia Stadium, passed a medical at the Amex Arena and is available to make his debut in Saturday's npower Championship trip to Sheffield Wednesday.
Boss Gus Poyet told seagulls.co.uk: "Everybody knows we have been looking for a player in that position. When we had the chance to bring a player with the quality of Matt until the end of the season we went for him.
"He's experienced, he's been a regular Premier League player and there were no doubts about it. He has presence, he's a leader as well and it's a good opportunity for us to use him the right way and for him to play football.
"Wayne Bridge knows him well from England and he's delighted as well. It should be very easy for them to play together. These opportunities don't come along very often so we had to take it and we hope to have him ready for Saturday.
"The teams at the top of this league have very experienced players and that gives you the extra bit when you need it. That experience will be important and the rest of the players will learn a lot from him too."
The deal will cover any potential play-off matches for Albion at the end of the season.
Upson said: "It's a really good opportunity for me. I have not been playing as much football as I would have liked this season. It's a chance for me to play until the end of the season.
"I've heard lots of positive things about Gus and his management style and the whole package here at Brighton is very exciting for me."