Kovalchuk signed a two-year contract with Avangard Omsk of the KHL on Saturday.
Kovalchuk tallied an assist while logging 11:11 of ice time during Sunday's 2-1 round robin win over the Bruins.
Kovalchuk registered an assist, two shots on goal and four PIM in Sunday's 4-3 win over the Wild.
Kovalchuk will play alongside Lars Eller and Carl Hagelin on the third line when he makes his Capitals debut Tuesday against the Jets, Samantha Pell of The Washington Post reports.
The Capitals acquired Kovalchuk from the Canadiens in exchange for a 2020 third-round pick.
Kovalchuk had four shots, two hits and one blocked shot in Saturday's 4-3 loss to the Stars.
Kovalchuk scored the overtime goal in Saturday's 2-1 win versus Toronto.
Kovalchuk had an assist and two hits in Sunday's 4-3 loss to the Blue Jackets.
Kovalchuk scored a goal on two shots and added two hits in Thursday's 3-1 win over Buffalo.
Kovalchuk had two goals in a 4-1 win over Philadelphia on Thursday.