The musician was found at his home in Hawick in the Scottish Borders on Thursday after a suspected heart attack.
Renbourn teamed up with fellow musicians, including guitarist Bert Jansch who died in 2011, to form Pentangle in the late 1960s.
His manager, Dave Smith, said Renbourn had been "a huge character".
He said: "He was always playing and teaching.
"That is what he loved doing and he never stopped."
Among those paying tributes to London-born Renbourn were DJ Cerys Matthews who said: "So sorry and sad to hear of John Renbourn's passing.
"A loving, lovely man.
"RIP John, it was an honour and pleasure meeting you."
Novelist Ian Rankin tweeted: "Ach, and now John Renbourn has died. What a guitarist."
Influential folk guitarist John Renbourn has died aged 70.