The 68-year-old Dutchman was appointed in March, when the Black Cats were one point above the relegation zone.
He guided them to safety and was due to leave the club in the summer, only to sign a new one-year contract.
Advocaat said: "I have made the decision to go after only eight games as I felt it was important to give everyone time to turn things around."
Sunderland chairman Ellis Short said: "I am truly saddened by Dick's decision, but I respect him for his honesty.
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"It is also testament to his character that he has foregone any kind of a financial settlement, something which is very unusual in football."
Assistant head coach Zeljko Petrovic has also left the club.
Saturday's draw with West Ham left Sunderland without a win in their first eight league matches and looking for a sixth manager in four years.
Since Steve Bruce was sacked in November 2011, Martin O'Neill, Paolo di Canio, Gus Poyet and Advocaat have managed the club.
Advocaat's departure also follows a trend set by Di Canio and Poyet of managers arriving to save the Black Cats from the drop, only to depart in the next season.
He initially agreed to lead Sunderland only until the end of last season, shedding tears as their survival was secured with a 0-0 draw at Arsenal.
Advocaat said he would leave the club to fulfil a promise to his wife, but changed his mind and returned in June.
The former Netherlands, Russia and South Korea boss has seen his side win just once this season - against League Two Exeter in the League Cup.
North-east rivals Newcastle are the only team below them in the Premier League table.
Dick Advocaat has resigned as Sunderland boss, with the team yet to win in the Premier League this season.