The 31-year-old has joined the Baggies on a free transfer and has signed a two-year contract with the club.
Lindegaard has long been expected to leave United after falling down the pecking order at Old Trafford.
Lindegaard told the club’s official website: “Since moving to England I’ve been impressed with how well West Brom have done in the Premier League.
“I had a good chat with Tony Pulis and he convinced me it would be a good move for me and the club. From there things moved very quickly. I was very keen to get it done so I can just concentrate on the thing that matters most, the football.”
