During his career, he played in over 1,300 National Hockey League (NHL) games over 18 seasons for the New York Rangers, Pittsburgh Penguins, Montreal Canadiens, Ottawa Senators, and Florida Panthers between 1992 and 2013.

Best known for his stickhandling skills, deking ability and wrist shot, he became an important part of the Rangers' 1994 Stanley Cup run, finishing with the third-most points for New York in the 1994 playoffs.

[2] During the 1994–95 NHL lockout, Kovalev returned to Russia to play for his hometown team Lada Togliatti, the defending International Hockey League champion from 1994.

[citation needed] Just 14 games into the 1998–99 season, on November 25, 1998, Kovalev was traded, along with Harry York, to the Pittsburgh Penguins in exchange for Petr Nedvěd, Sean Pronger and Chris Tamer.

He was sent, along with Dan LaCouture, Janne Laukkanen and Mike Wilson, for Mikael Samuelsson, Rico Fata, Joel Bouchard, Richard Lintner and cash.

Kovalev spent the 2004–05 NHL lockout playing for Ak Bars Kazan, in the Russian Superleague (RSL), where he registered 23 points in 35 games.

As an unrestricted free agent, Kovalev opted to re-sign with Montreal on a four-year contract paying $4.5 million annually just prior to the start of the 2005–06 season, on August 3.

In 2007, Kovalev sparked controversy when he allegedly criticized his team, coaching staff and the Montreal media in an interview with a Russian reporter in his native language.

[4] Due to his inspired play, Kovalev was awarded the Canadiens' captaincy on two occasions during the season, replacing the injured Saku Koivu in his absence.

On February 24, 2011, his 38th birthday, Kovalev waived his no-trade clause to be traded back to the Pittsburgh Penguins in exchange for a conditional seventh-round draft pick.

[13] After failing to sign with an NHL team for the 2011–12 season, Kovalev returned to Russia to play with the Atlant Moscow Oblast in the Kontinental Hockey League (KHL).

[14] In June 2012, he was released from the two-year deal he signed with Atlant Moscow Oblast, at which point he declared his desire to return to the NHL.

Swiss National League B (NLB) team EHC Visp announced on June 10, 2013, that they had signed him to a one-year contract with an option for a second year.

[22] Kovalev made a return to professional ice hockey on October 18, 2016, playing again for EHC Visp, the team he has become general manager of, after forward William Rapuzzi became injured before the day of the game.