The Toffees accepted a bid for the 26-year-old Russia winger on Wednesday and he had travelled to his homeland to discuss personal terms and undergo a medical.
He made 77 appearances for Everton, scoring nine goals, but failed to make himself a regular starter for David Moyes' side.
Moyes admitted the signing of Bilyaletdinov, who had made only seven starts this season, had not quite worked out as he had hoped.
"He was a great boy to work with, a really good professional," he told the club's website.
"When he played, he was totally committed and he did everything he could to succeed. We wish him well. It just didn't quite work and obviously we've decided to sell.
"It happens. You could probably ask every manager in the Premier League about players and I can think of some clubs you could ask about a lot of players but, yes, Bily's been in here and not quite reached what we wanted.
"But I couldn't fault anything that he did - he is a good lad."
