Tuesday's announcement came after a 24-year-old man claimed he began a sexual relationship with Clash when he was 16.
The alleged victim is reported to have received a $125,000 settlement to recant his story, but later told TMZ he felt pressured into the deal and was looking for a way to get out of it because he wasn't lying.
Clash has denied the man's allegations and last week took a leave of absence from his job to deal with the fallout from the scandal.
Another 24-year-old man has since come forward, claiming he began a sexual relationship with Clash after meeting him on a gay phone chat line in 2003, TMZ reported. He is suing Clash for $5 million, the website said.
Sesame Workshop said Tuesday Clash isn't coming back to the show.
"Sesame Workshop's mission is to harness the educational power of media to help all children the world over reach their highest potential," Sesame Workshop said in a statement issued to The Hollywood Reporter. "Kevin Clash has helped us achieve that mission for 28 years, and none of us, especially Kevin, want anything to divert our attention from our focus on serving as a leading educational organization.
"Unfortunately, the controversy surrounding Kevin's personal life has become a distraction that none of us want, and he has concluded that he can no longer be effective in his job and has resigned from 'Sesame Street.' This is a sad day for 'Sesame Street.'"
"I am resigning from Sesame Workshop with a very heavy heart. I have loved every day of my 28 years working for this exceptional organization," Clash, 52, said in a statement to People.com Tuesday. "Personal matters have diverted attention away from the important work 'Sesame Street' is doing and I cannot allow it to go on any longer. I am deeply sorry to be leaving and am looking forward to resolving these personal matters privately."