Clemence, who won three European Cups and five First Division titles during a trophy-laden spell at Anfield, was arguably one of the greatest goalkeepers of his generation.
He won 61 England caps, which would undoubtedly have been many more had he not been competing with Peter Shilton, who accumulated 125, for the number one shirt.
An £18,000 signing from Scunthorpe by Bill Shankly, Clemence was a key member of the Liverpool team which dominated Europe between 1977 and 1981, and also picked up two UEFA Cups, an FA Cup and the League Cup.
At Tottenham, whom he joined in 1981 aged 32 for a fee of £300,000, he won another UEFA Cup and FA Cup.
"With great sadness, we write to let you know that Ray Clemence passed away peacefully today, surrounded by his loving family," said a statement from the Clemence family.
"After fighting so hard, for such a long time, he's now at peace and in no more pain.
"The family would like to say a huge thank you, for all the love and support that he's received over the years.
"He was loved so much by us all and he will never be forgotten."
Clemence is survived by his wife Veronica, son Stephen – a former player himself and now a coach – and daughters Sarah and Julie.