The body of Ola Brunkert, who lived alone in Majorca, was found in a pool of blood by a neighbour in his garden late on Sunday.
Police said he appeared to have fallen through a window. Spanish media said the first results from an autopsy confirmed the death was accidental.
The media also quoted the Major of Arta, where he lived, as saying Brunkert had been depressed for some months following the death of his wife.
The Swede worked as a session drummer with Abba and also toured with the group.
Abba’s Benny Andersson told the Swedish daily newspaper Expressen that it was ”tragic news.”