He was a key member of Clough's all-conquering Forest team, assisting Trevor Francis' winner in their 1979 European Cup final victory over Malmo before scoring himself to sink Hamburg in the 1980 final.
"We are heartbroken to announce the passing of Nottingham Forest legend and dear friend, John Robertson," Forest said in a statement.
"A true great of our club and a double European Cup winner, John’s unrivalled talent, humility and unwavering devotion to Nottingham Forest will never ever be forgotten."
Robertson spent most of his career at the City Ground, making over 500 appearances across two stints at the club.
Clough once described him as a "scruffy, unfit, uninterested waste of time" who became "one of the finest deliverers of a football I have ever seen", usually with his cultured left foot.
Robertson was a stalwart of Forest's meteoric rise from the second division to winning the English first division title the following season in 1978, before the two European Cup triumphs.
He earned 28 caps for Scotland, scoring the winning goal against England in 1981, and served as assistant manager to former Forest teammate Martin O'Neill at several clubs, including Aston Villa.
"Rest in peace, Robbo… Our greatest," Forest said.
