The 33-year-old, who struggled for first-team minutes at boyhood club Liverpool, has signed a two-year deal upon after just one season at Anfield to complete a £3 million move.
West Brom has completed the signing of Rickie Lambert from Liverpool on a two-year deal.
The striker only moved to Anfield from Southampton last summer, but struggled with the pressure of playing for his boyhood club as he scored just two Premier League goals in limited first-team exposure.
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.