The abattoir, which had employed almost 100 people, shut down last year after going into receivership.
Administrator Grant Thornton confirmed the sale of the land and buildings had been completed, but would not reveal the name of the buyer.
A spokesman for Anglesey Council said it understood that a private company had bought the site. "We understand the site has been sold to a private company - this is a key site on the Llangefni industrial estate," he said.
"We look forward to hearing the new company's plans and to co-operating with them in developing and regenerating the area further."