Huddersfield defender Murray Wallace has signed a new contract that will keep him at the club until the summer of 2017.
Nottingham Forest have signed Tom Ince on loan from Hull City on a deal until December 28.
Former Croatia, Everton and West Ham manager Bilic, 44, took charge of Lokomotiv last summer but could only guide the club to a ninth-placed finish in the 16-team Premier League - the club's worst finish since 1991.
A statement on Lokomotiv's official website said Bilic's contract had been cancelled by mutual consent.
His replacement Kuchuk, 53, is the former manager of Kuban Krasnodar, Salyut Belgorod and Sheriff Tiraspol.