Clash responded that he is "relieved that this painful allegation has been put to rest".
Sesame Workshop, which produces Sesame Street, followed by saying: "We are happy that Kevin can move on from this unfortunate episode."
The whirlwind episode began on Monday, when Sesame Workshop startled the world by announcing that Clash had taken a leave of absence in the wake of allegations that he had had a relationship with a 16-year-old boy.
Clash, a 52-year-old divorced father of a grown daughter, swiftly denied the charges of his accuser, who is in his early 20s. Clash acknowledged that he was 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 the accuser twice. 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 yesterday 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 rivalled Big Bird as the face of Sesame Street.
Though usually behind the scenes, Clash achieved his own measure of fame, publishing a 2006 autobiography, My Life As A Furry Red Monster.