The 30-year-old full-back will stay on loan with the Hammers until the end of the season.
“I am delighted to sign for West Ham United,” Bridge told West Ham’s official website.
“I am just looking forward to meeting everyone at the training ground, starting work and getting out on the pitch and playing in front of the fans. I am glad the loan is sorted and I’m ready to play.
“It will be great to play a part in helping keep West Ham in the Premier League – it would be a big achievement.”
He added: “I know a few of the players from England and I know the physio. I spoke to Scotty Parker and a few people and they told me what a great club it is. That definitely helped me make the decision to come here.
“There is a lot of quality here and I know we can move up the table. The first half on Tuesday was great. There should have been a few more goals and then the team came back with ten men. If we can play like that every week we’ll be fine.”