The striker only moved to Anfield from Southampton last summer, his boyhood club, but struggled with limited first-team exposure and scored just two Premier League goals.
Lambert tasted Premier League football for the first time with Southampton in 2012-13, scoring 13 times and earning a call-up to the senior England squad, before an improved return of 15 goals the following campaign.
The 33-year-old underwent a medical earlier on Friday and has now completed a £3 million move.
"Rickie is a good, strong, solid player who is a great character, good in the dressing room and good on the pitch," manager Tony Pulis told the club's official 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."
