The players will wear black armbands in Saturday afternoon's game at Stoke in tribute to Campbell, who was Blues boss from 1988 to 1991 and guided the club to promotion back to the top flight in 1989 at the first time of asking.
"Chelsea Football Club is greatly saddened to announce the passing of our former manager Bobby Campbell at the age of 78," the Barclays Premier League champions said
"All at the club send our deepest condolences to Bobby's family and friends and our players will wear black armbands in his memory at today's game at Stoke."
T he west London club added: " Chelsea was very close to Bobby Campbell's heart and he will always be close to ours."
Campbell began his playing career with his local side Liverpool, before stints with Wigan, Portsmouth and Aldershot.
He returned to Pompey for his first coaching experience and also had spells on the coaching staff at QPR, Arsenal and Fulham.
He was promoted to manager at Craven Cottage in 1976 and stayed in the role until October 1980, working alongside players such as George Best and Bobby Moore.
Further managerial spells with Portsmouth and then Chelsea followed, in addition to coaching roles back with Aldershot and QPR.
Tributes were pouring in on Saturday from many of Campbell's other former clubs
"Everyone at Fulham Football Club was saddened to learn of the passing of former manager Bobby Campbell," a statement from the Cottagers read
"The thoughts of all at Fulham are with Bobby's family and friends at this sad time."
Pompey tweeted: "Portsmouth Football Club are saddened to learn of the death of former #Pompey player and manager Bobby Campbell #RIPBobby."
Arsenal posted: "Everyone at @Arsenal send their thoughts and wishes to family and friends of former first-team coach Bobby Campbell following his sad death."
QPR said: "QPR are saddened to hear of the passing of former assistant manager Bobby Campbell, who has died at the age of 78."
Source : PA