Campbell managed the London side from 1988 to 1991, leading them to promotion to the top flight of English football in 1989 and the following year to a fifth-place finish, Chelsea's best performance for 20 years.
The Liverpudlian also managed Fulham and Portsmouth and had coaching spells at Arsenal, Aldershot and QPR, and in Kuwait.
He began his playing career with his local club Liverpool and also played for Portsmouth and Aldershot.
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"Chelsea Football Club is greatly saddened to announce the passing of our former manager," they said in a statement.
"Our players will wear black armbands in his memory at today's game at Stoke.
"Chelsea was very close to Bobby Campbell's heart and he will always be close to ours."
(Reporting by Ian Chadband, editing by Ed Osmond)
