Arthur Cave, 15, was found with life threatening injuries by members of the public at the bottom of the cliff at Ovingdean Gap on Tuesday evening.
He was taken to the Royal Sussex County Hospital in Brighton, where he later passed away.
A Sussex Police spokeswoman said: "A 15-year-old boy who was found with life threatening injuries on the underpass of Ovingdean Gap, having fallen from the cliff above, has sadly died in hospital.
"Members of the public carried out first aid on the boy before he was taken to hospital just after 6pm.
"He later died there of his injuries.
"The death is being dealt by the coroner's officer."
His death is not being treated as suspicious, they confirmed.
Meanwhile Bad Seeds singer Nick Cave and his wife Susie Bick, who live in East Sussex, have issued a statement on behalf of their family.
It read: "Our son Arthur died on Tuesday evening. He was our beautiful, happy loving boy.
"We ask that we be given the privacy our family needs to grieve at this difficult time."
Arthur had a twin brother named Earl.
Our thoughts are with his family at this tragic time.