The experienced defender, who has also played for QPR, Wolves, Nottingham Forest and Hamburg, brings a lot of knowledge to the Albion squad.
"We've been looking for a centre back throughout the whole of the transfer window," said Hasselbaink in a statement.
"He has lots of experience and has played lots of games in higher leagues.
"I'm very happy that he is signing with us."
Mancienne told the club's website: "It's obviously a pleasure to be here and I'm really grateful that the manager has given me the opportunity to join and help with the battle.
"I know how to see out games and what the team has to do to win games, so I hope to bring that experience with me."