Lev Yashin Dynamo Academy prospects inked contracts till June 2026.
Kutitsky, who turns 21 on January 1, made his debut for the first team in February 2021 and since then played 28 matches and scored 1 goal.
Gladyshev has also been playing for the White-Blues' main team since last year. The 19-year-old forward scored 5 goals and made 4 assists in 28 appearances.
Both footballers debuted for Russia U-21 in September.