The 28-year-old took the captaincy from Dustin Brown, who captained the team since 2008, to become the 14th captain in history of the Los Angeles Kings.
Kopitar, who will be playing his 11th season for the team in the autumn, also recently signed an extension worth US$80m over eight years.
He said on his website that getting the captaincy of the Los Angeles Kings was a "great honour, and at the same time a great responsibility".
Kopitar said he would not be changed by the honour. "I have never been burdened by any leadership. You need to play your game, you need to express your character and this will be so also in the future," he added.
The Slovenian was the most efficient player for the club last season, collecting 74 points in 81 games. He also scored five points in four games in the play-offs.