Murray announced his decision to resign on Tuesday, after the Seattle Times reported that his younger cousin told the newspaper that the mayor repeatedly molested him as a teenager in the 1970s.
"I am just so happy", said Simpson, 49, one the first people to publicly accuse Murray of sexual abuse.
That fifth accuser is Murray's cousin's son.
Ed Murray, 62, a Democrat, is the city's first openly gay mayor.
City council president Bruce Harrell will become mayor in the interim, and he has five days to decide whether he will fill the remainder of Murray's term until Durkan or Moon take over in January.
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As a effect of Murray's resignation, whoever wins the Seattle mayoral contest (almost certainly either Jenny Durkan or Cary Moon) will become the city's next leader as of the certification of the November 2017 general election in late November... a month prior to when Murray's term was set to end.
Murray denied those allegations, blaming them on a "family rift". That prompted OR child-welfare officials to conclude Murray should never again be a foster parent.
"I have no assets, I have no investments and if I lose, everything I have done, everything I have worked for, the most important thing to me - my integrity - it'll be gone", Murray said in an interview with Brandi Kruse at Q13 in April.
Amusing how the very minor story of a top Dem mayor resigning in disgrace after five sex abuse allegations doesn't get as much play as a rogue "like" by whoever was running Ted Cruz's account.
Durkan, a former US attorney, said her campaign shouldn't be tainted by Murray's endorsement of her candidacy and the allegations against him, adding that she has a squeaky clean background and vowing that there would be no scandals if she is elected mayor.
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'It is time for Mayor Murray to step down, ' Durkan said in a new statement.
In July, the Seattle Times uncovered a CPS report about his alleged abuse that was previously believed to have been destroyed.
Seattle's Mayor Ed Murray has resigned after he was accused of sexual abuse - again.
On Tuesday, Simpson said, "If nothing else happens, and nothing else comes of it, for me, I will be OK". She amended her view Tuesday, shortly before the mayor's announcement. He was also accused of sexual assault in 1984, but charges were not filed. Murray, a former Democratic state legislator, had said in May that he would not seek re-election and would retire from politics at the end of the year when his term ends. "I don't know. But this definitely - this is a major step in the right direction".
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