The 31-year-old goalkeeper has spent the last five seasons of his career with Man United, making 29 appearances for the club.
The Danish international revealed that he is optimistic about West Brom’s future while complimenting manager Tony Pulis.
“Since moving to England I’ve been impressed with how West Brom have done in the Premier League,” Lindegaard said to the official West Brom website.
“I had a good chat with Tony Pulis – I must call him the ‘gaffer’ now – and he convinced me it would be a good move for me and the club.”
Lindegaard struggled for first-team action at Old Trafford, and he became surplus to requirements after Sergio Romero won the starting job for the 2015-16 season.
Sam Johnstone was preferred as Romero’s back-up this season, leaving Lindegaard no choice but to exit the club.
Lindegaard is the third Man United player to depart Old Trafford on Monday, as Adnan Januzaj and Javier Hernandez heading to Borussia Dortmund and Bayer Leverkusen respectively.