Depp has cited the guitarist as the inspiration behind his swashbuckling Pirates of the Caribbean character Jack Sparrow and the pair even starred as father and son in the franchise's third installment in 2007.
However, Depp failed to make an impression on his idol at their first meeting - the rocker just thought he was a friend of his son Marlon.
Richards recalls, "It took me two years before I realized who he was. He was just one of my son Marlon's mates, hanging around the house playing guitar. I never ask Marlon's mates who they are, because you know, (they say) 'I'm a dope dealer'."
"Then one day he was at dinner (eating with a knife and fork) and I'm like, 'Whoa! Scissorhands!' Then I find out he's an actor, and like one of the biggest Keith Richards fans in the world - and how do I deal with that? 'Get over it, Johnny.'"