Sidibe, 20 on July 29, impressed for Ligue 2 club Troyes last season as they sealed promotion to the top flight.
He had been courted by Lyon as well as Lille, with the transfer announced on Troyes’ website.
“We understand the wishes of Djibril and we would like to give him our best wishes for the rest of his career,” the statement added.
The fee is understood to be in the region of 2 million euros.
France defender Debuchy, 26, has been linked with both Newcastle and Inter, expressing a preference to join the former in the Premier League.
Lille had said they would only sell if they found a suitable replacement.