Varlamov, 24, joined Lokomotiv's organization at age 11 and played two seasons for the KHL team before moving to North America with the Washington Capitals in 2008. The Capitals traded him to Colorado last summer.
Varlamov led Russia to the gold medal at the World Championship in May.
Kulikov, 21, is a restricted free agent with the Panthers who had four goals and 28 points last season.
Lokomotiv spent the past year assembling a team for its return to the KHL after the entire roster was killed last September in a plane crash that left 44 people dead.