The Russian Football Union (RFU) stressed Fabio Capello remains under contract with the national team.
The Northern Ireland striker has signed a three-year deal after rejecting the chance to 'transfer' to the newco Rangers.
Lafferty, who joined Rangers from Burnley in 2008, played more than 100 times for the Light Blues.
A statement on the Swiss club's official website announced his three-year contract, adding: "He will be presented at a press conference on Monday, then will join his new team-mates for training.''
Lafferty is the latest player to leave the financial troubles at Ibrox behind.
Steven Whittaker also left Glasgow on Saturday, opting to join Norwich on a four-year deal.