Ed Murray, 62, who had already confirmed he would not be seeking a second term, will step down effective of 5:00 pm today (0000 GMT Thursday).
"While the allegations against me are not true, it is important that my personal issues do not affect the ability of our city government to conduct the public's business," he said in a statement.
Joseph Dyer, a 54-year-old dialysis technician, said Murray forced him into sex for about a year while the two shared a bedroom in the New York home of Dyer's mother when the alleged victim was 13, according to The Seattle Times.
"And that's when he would molest me. And my mother would be right there in the house, she'd be in the living room... watching TV."
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The molestation stopped, Dyer said, when a boy in a Catholic group home where Murray worked accused him of abuse.
Dyer told the newspaper he wanted the mayor punished, although Murray attributed the accusation to a rift in the family.
The mayor said it had nevertheless become clear that it was "best for the city" that he resign.
Four men had previously accused Murray, who denies any wrongdoing, of sexually abusing them.
A lawsuit was filed in King County Superior Court in April on behalf of one of the accusers, now 46, who said the mayor paid him for sex when the alleged victim was a drug- addicted, homeless 15-year-old.
Another alleged victim, a 49-year-old resident of Portland, in the neighboring state of Oregon, went on television to accuse the progressive and openly homosexual Democratic politician of sexual assault.