In a quick turnabout, the man on Tuesday described his sexual relationship with Clash as adult and consensual.
Clash responded with a statement of his own, saying he is "relieved that this painful allegation has been put to rest." He had no further comment.
The man, who has not identified himself, released his statement through the Harrisburg, Pa., law firm Andreozzi & Associates.
Sesame Workshop, which produces "Sesame Street" in New York, soon followed by saying, "We are happy that Kevin can move on from this unfortunate episode."
The whirlwind episode began Monday morning, when Sesame Workshop startled the world by announcing that Clash had taken a leave of absence from "Sesame Street" in the wake of allegations that he had had a relationship with a 16-year-old.
Clash, a 52-year-old divorced father of a grown daughter, swiftly denied the charges of his accuser, who is in his early 20s. In that statement Clash acknowledged that he is gay but said the relationship had been between two consenting adults.
Though it remained unclear where the relationship took place, sex with a person under 17 is a felony in New York if the perpetrator is at least 21.
Sesame Workshop, which said it was first contacted by the accuser in June, 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.
Clash said on Monday he would take a break from Sesame Workshop "to deal with this false and defamatory allegation."
Neither Clash nor Sesame Workshop indicated on Tuesday when he might return to the show, on which he has performed as Elmo since 1984.
Elmo had previously been a marginal character, but Clash, supplying the fuzzy red puppet with a high-pitched voice and a carefree, child-like personality, launched the character into major stardom. Elmo soon rivaled Big Bird as the face of "Sesame Street."
Though usually behind the scenes, Clash meanwhile achieved his own measure of fame. In 2006, he published an autobiography, "My Life as a Furry Red Monster," and he was the subject of the 2011 documentary "Being Elmo: A Puppeteer's Journey."
He has won 23 daytime Emmy awards and one prime-time Emmy.