Arthur Cave (15), who had a twin brother Earl, was found with life-threatening injuries on the underpass of Ovingdean Gap at 6pm on Tuesday (local time).
He died later that evening of his injuries in hospital.
The death is not being treated as suspicious, but police sources have reportedly described it as accidental.
His parents Nick and Susie Cave have paid tribute to their son.
They said: "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."
On Wednesday, his twin brother Earl left flowers and a message on the beach, Britain's Daily Telegraph reported.
The note read: "Arthur - I love you so much. You were a joy to be around and I will never forget you. You were the best brother I could ever ask for. Earl."
