Hope was part of the sides that won the 1966 League Cup and 1968 FA Cup in a career that saw him play 409 times for the club from 1960 to 1972.
The midfielder scored 42 times for the Baggies and also won seven caps for Scotland.
Hope also played for Birmingham City, Sheffield Wednesday and Bromsgrove Rovers, while also managing the latter, leading them to second place in the equivalent of the National League.
The Albion favourite spent time on loan at the Philadelphia Atoms and Dallas Tornado in the United States. He also worked as chief scout at The Hawthorns in 2000.
"The thoughts of all at the club are with Bobby's family, friends and team-mates at this desperately sad time," a West Bromwich Albion statement read.
"The club will pay a full tribute to Bobby and will honour his Albion legacy at the first home game of the 2022-23 season."