The 31-year-old Denmark international joined Albion on a free transfer after passing a medical at the Hawthorns.
"Since moving to England I've been impressed with how well West Brom have done in the Premier League," Lindegaard told the club's website (www.wba.co.uk) on Monday.
Lindegaard joined United in 2010 from Norwegian side Aalesund but made only 29 first-team appearances for the Old Trafford club, acting as back-up for Edwin van der Sar and David De Gea.
He is the third United player to join West Brom this year after midfielder Darren Fletcher and defender Jonny Evans.
(Reporting by Ed Osmond; Editing by Tony Jimenez)
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