The family said in a post on Lee's website he had undergone routine surgery but did not say what the operation was for, the BBC reported.
"We have lost a wonderful and much loved father and companion, the world has lost a truly great and gifted musician," his wife and daughters said in a statement.
The network noted Lee, born in Nottingham, England, had earned acclaim for his guitar solos at the seminal Woodstock rock festival in New York state in 1969.
Ten Years After recorded eight albums that reached the Top 40 in the United Kingdom. The band's biggest hit, "I'd Love To Change the World," came in 1971.
The BBC said Lee released his 14th record, "Still on the Road to Freedom," last August.
He was to have played a concert at Olympia Hall in Paris Thursday with blues guitarist Johnny Winter.