According to Dutch newspaper Het Parool, the former player reportedly “sent images of his genitals along with the messages.”
In a statement released by the club, Overmars explains his decision to leave, saying he is “ashamed” of his actions.
“Last week I was confronted with reports about my behavior,” he said to the Ajax website. “And how this has one across to others.”
“Unfortunately, I didn’t realise that I was crossing the line with this, but that was made clear to me in recent days.”
He added: “Certainly for someone in my position, this behavior is unacceptable. I now see that too. But it is too late. I see no other option but to leave Ajax.”
Overmars had been in his position since 2012, and recently signed a contract extension until 2026.
“I find the situation appalling for everyone,” said CEO Edwin van der Sar. “In my role, I also feel responsible to help colleagues. A safe sport – and working climate is very important. We will pay even more attention to this in the near future.”
Ten Hag has long been linked to the managerial vacancy at Manchester United.