Murray, a Democrat and the city's first openly gay mayor, said he was resigning effective 5 p.m. Wednesday so the scandal would no longer overshadow his office.
Murray denied the allegations, as he has in the past. Previously, he called them part of a political effort to stymy his progressive agenda and support for LGBTQ and immigrant rights.
"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.
"To the people of this special city and to my dedicated staff, I am sorry for this painful situation."
Council President Bruce Harrell will become mayor upon Murray's resignation. Harrell has five days to decide to hold the position for the remainder of Murray's term, which ends in December.
Murray, 62, was elected in 2014 after 18 years as a state lawmaker. In his statement Tuesday, he touted his accomplishments from his political career. As an openly gay state legislator, he sponsored Washington state's historic marriage equality law and a landmark bill banning discrimination based on sexual orientation.
But, in light of the latest allegations, he said it was clear it is best for the city for him to step aside.
Delvonn Heckard said he was 15 and Murray was 32 when the sexual acts occurred, claiming that Murray paid him for them.
The complaint further alleged that Heckard was not the only child abused by the mayor. On at least one occasion, Heckard said he was at Murray's apartment when another boy who appeared underage was there. "D.H. was of the understanding that Mr. Murray was having sex with the other boy for money at the same time," the complaint alleged. A spokesman for the mayor said the allegations were unfounded.
Since the lawsuit, four more men have publicly accused Murray of various forms of sexual abuse when they were teens. CNN has not