He won 10 major honours as a player in British and European football.
The Edinburgh-born player also won 22 caps for his country and was named 'Footballer of the Year' in both Scotland and England.
Paying tribute, Spurs said: "He was one of our greatest ever players and a man who never failed to inspire those around him."
Dave Mackay Spurs paid tribute to "a man who never failed to inspire those around him".
After winning all three domestic honours in Scotland with Hearts, Mackay joined Spurs in 1959.
He helped the north London club become the first post-war team to achieve the double of league and FA Cup in 1961, then won the FA Cup again in 1962 and 1967.
Spurs described him as "the heartbeat" of their double-winning side and said he played a "vital role" in their 1963 European Cup Winners' Cup success despite missing the final through injury.