Police in the city of Malaga said Priscilla White (her real name) died in Estapona in the Costa del Sol region.
She appeared to have died from natural causes but this had not yet been confirmed by tests, police said.
Black's publicist confirmed her death in a brief statement.
"It is with deep sorrow that I confirm today the passing of singer and TV personality Cilla Black," Nick Fiveash said in an emailed statement.
"Details of her death will be announced following the coroner's report.