Nilsson, the Swedish soprano who set up the prize foundation, picked Domingo before her death in 2005, age 87.
Prize officials said on Friday that the name had been kept secret for three years after her passing at her request, reports The BBC.
As one of The Three Tenors, Domingo did much to popularise operatic singing.
The citation for the prize calls Domingo "one of the greatest opera singers of all time".
Nilsson performed with Domingo on several occasions throughout her career.
"Placido acquitted himself splendidly. He was an incredibly good Cavaradossi, his acting was superb - he was the part, he loved the part and on top there was gorgeous singing," she said later.
A prize ceremony is planned later this year in Stockholm. (ANI)