Barlow, who had been ill for some time, joined the Baggies at the age of 18 in 1944 and went on to play 482 times for the club, although only once for England.
He was the last surviving member of the team that won the FA Cup in 1954, beating Preston 3-2, and in 2004 was named as one of West Brom's 16 greatest players in a poll organised to mark the club's 125th anniversary celebrations.
A tribute on the club's official website read: "The great Ray Barlow stands at the pinnacle of the club's story, one of a handful of truly world-class footballers that Albion have produced over 130 years and more of existence.
"Ray Barlow will forever be a cornerstone of the football club, one of its true legends, one of the foundations upon which Albion are built. We will never see his like again. Our thoughts are with his family and friends."