The 67-year-old Dutchman said he no longer wished to continue a career in club management.
He joined the Black Cats until the end of the season in March, replacing the sacked Gus Poyet, with the side one point above the relegation zone.
“Sunderland has been one of the highlights of my career,” he said.
“At certain moments in your life you have to make a decision and I am almost 68 years old now.
“A number of clubs contacted me but the decision was always Sunderland or nobody.”
Advocaat wept as he secured Sunderland’s Premier League survival with a goalless draw at Arsenal in their penultimate game of the season.
Sunderland chairman Ellis Short said: “Although I am extremely disappointed, I understand and absolutely respect his decision.
“In his brief time here he made a real impact and lifted the club with his experience and enthusiasm. We will always be grateful to him for what he achieved.” — BBC