Lambert, who has 11 caps for England, leaves Merseyside for an undisclosed fee, estimated to be around 3 million pounds ($4.7 million), according to British media reports.
The forward never established himself at Liverpool, scoring only three times in 36 appearances, and had fallen down the pecking order following the arrivals of strikers Christian Benteke, Divock Origi and Danny Ings in the close season.
"Rickie is a good, strong, solid player who is a great character, good in the dressing-room and good on the pitch," West Brom manager Tony Pulis told the club website.
"We are very pleased to have him on board.
"He's a player of great pedigree and we look forward to integrating him into our squad."
Lambert, 33, started his career in Liverpool’s academy and, after spells at several lower league clubs, joined Southampton where he scored 117 goals in five seasons, including 28 in two campaigns in the Premier League.
He was part of England’s World Cup squad in Brazil and earned a move to Liverpool, but struggled to claim a regular place at Anfield despite the club's struggles up front last season.
He was frequently left on the bench as Liverpool manager Brendan Rodgers often chose to use Raheem Sterling in a lone centre forward role, even though it was not his preferred position.
He is likely to get far more first-team opportunities under Pulis, whose side begin their Premier League campaign at Manchester City on Aug. 10.
(Reporting by Toby Davis; editing by xxx)
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