The England striker passed a medical at the Hawthorns, a year after he joined the Reds from Southampton.
Lambert would have faced tough competition for a starting place at Anfield next season following the arrival of Christian Benteke, Danny Ings and Roberto Firminho.
The forward had just two Premier League goals to his name from 25 games for Liverpool last season, 18 of those off the substitutes’ bench.
But the 33-year-old was more prolific at Southampton where he totalled 106 goals from 207 league appearances from August 2009 until June 2014.
“Rickie is a good, strong, solid player who is a great character, good in the dressing room and good on the pitch,” West Brom head coach 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.”