He was selected 53rd overall in the 2019 CHL Import Draft by the Saginaw Spirit of the Ontario Hockey League (OHL) and made his North American major junior debut in the following 2019–20 season, where he scored seven goals and had 33 assists for 40 points in 53 games.

He was drafted in the seventh round, 205th overall, in the 2020 NHL Entry Draft by the Calgary Flames and returned to Belarus to play with HC Dinamo Minsk of the Kontinental Hockey League (KHL).

As a rookie in the 2020–21 season, Solovyov recorded 2 goals and 7 assists for 9 points and 36 penalty minutes in 41 games.

Solovyov was signed to a three-year, entry-level contract with the Calgary Flames on 6 April 2021.

[1] [2] Before the start of the 2024–25 NHL regular season, Solovyov re-signed with the Flames on a two-year contract on 19 September 2024 as a restricted free agent.