Clash, the 52-year-old divorced father of a grown daughter, acknowledged that he is gay in that statement.
Sesame Workshop, which said it was first contacted by the accuser in June, said it had launched an investigation that included meeting with the accuser twice and meeting with Clash. Its investigation found the charge of underage conduct to be unsubstantiated.
The next day Clash's accuser recanted his charge, describing his sexual relationship with Clash as adult and consensual. Clash responded that he was "relieved that this painful allegation has been put to rest."
In addition to his marquee role as Elmo, Clash had served as the show's senior Muppet coordinator and Muppet captain. He won 23 daytime Emmy awards and one prime-time Emmy.
In 2006, he published an autobiography, "My Life as a Furry Red Monster," and was the subject of the 2011 documentary "Being Elmo: A Puppeteer's Journey."
Though it remained unclear who might take over for Clash performing as Elmo, other "Sesame Street" puppeteers have been trained to serve as his stand-in, Sesame Workshop said.
"Elmo is bigger than any one person," the company said last week.