In a statement of his own, Clash, 52, the puppeteer and voice behind popular red Muppet Elmo, said, "I am relieved that this painful allegation has been put to rest. I will not discuss it further."
There was no word Tuesday afternoon on whether Clash would cancel the leave of absence he has taken from "Sesame Street" since news of the relationship surfaced.
Sesame Workshop said in a statement: "We are pleased that this matter has been brought to a close, and we are happy that Kevin can move on from this unfortunate episode."
On Monday, Sesame Workshop issued a statement saying that the man had contacted them in June saying he and Clash began a relationship seven years ago, when the unidentified man was 16.
"We took the allegation very seriously and took immediate action," that statement read. "We met with the accuser twice and had repeated communications with him. We met with Kevin, who denied the accusation. We also conducted a thorough investigation and found the allegation of underage conduct to be unsubstantiated. Although this was a personal relationship unrelated to the workplace, our investigation did reveal that Kevin exercised poor judgment and violated company policy regarding Internet usage and he was disciplined."
In a statement to NBC News issued Monday, Clash said the man was of age when the relationship began.
"I am a gay man. I have never been ashamed of this or tried to hide it, but felt it was a personal and private matter," Clash said. "I had a relationship with the accuser. It was between two consenting adults and I am deeply saddened that he is trying to characterize it as something other than what it was. I am taking a break from Sesame Workshop to deal with this false and defamatory allegation."
Clash has performed with "Sesame Street" characters since 1979, when he played Cookie Monster in the Macy's Thanksgiving Day Parade. He became an official puppeteer on "Sesame Street" in 1984 and created character voices for puppets such as Baby Natasha and Dr. Nobel Price.
Clash was not the first puppeteer to voice Elmo, but once he took over the character in 1985 and gave it a high-pitched toddler voice, the character became enormously popular.
Clash was the subject of the 2011 documentary "Being Elmo," which documented his lifelong love of puppeteering.
"Elmo is bigger than any one person and will continue to be an integral part of 'Sesame Street' to engage, educate and inspire children around the world," said Sesame Workshop.
More in The Clicker:
- Lea Michele: Dog pee wrecked my spray tan
- Jenelle Evans admits getting high after rehab on 'Teen Mom 2' season premiere
- 'Dancing With the Stars' pro Derek Hough: A low score from Len is good for us
- 'Dancing With the Stars' judges melt down over Shawn's tribal trio