Brown had been the Kings' captain for eight seasons since 2008, raising the Stanley Cup in 2012 and 2014. But the American center's play has dipped markedly in recent years, and he has failed to score 30 points in the last four consecutive seasons.
The switch was announced by Dean Lombardi, the Kings' president and general manager.
Kopitar is the Kings' first-line center and their leading scorer for nine consecutive seasons. He has served as an assistant captain since 2008, but the Kings are tying their long-term future to the Slovenian playmaker.
Kopitar, who turns 29 later this summer, is the 14th captain in Kings history. He has an eight-year, $80 million contract with the Kings through 2023-24.
The 31-year-old Brown has a $47 million contract through 2021-22, and though he has capably managed the leadership aspects of his job, his on-ice production hasn't matched his financial compensation.
Brown was the Kings' first-round draft pick in 2003, while Kopitar was their first-round choice in 2005. They've been teammates since 2006 while spending their entire NHL careers with the Kings, persevering through several rough seasons before leading Los Angeles' rise to become a two-time Stanley Cup champion.
Both centers played major roles in the 2012 playoffs, when the eighth-seeded Kings rampaged through the postseason with a 16-4 record on the way to the franchise's first Stanley Cup title. Brown and Kopitar shared the postseason scoring lead with 20 points apiece in those 20 playoff games before Brown accepted the Stanley Cup from Commissioner Gary Bettman, becoming just the second American-born captain to raise the NHL's top prize.
Brown has yet to reprise the offensive production he showed in 2012, although he still showed a knack for big goals during the next two postseasons, when the Kings reached the Western Conference finals in 2013 and won it all again in 2014.
Brown's declining play has been a major topic of discussion in recent years around the Kings, who missed the playoffs entirely in 2015 with just 11 goals from Brown. The former captain's inability to generate offense while playing his usual physical game has hurt the Kings, although coach Darryl Sutter has always staunchly defended Brown's presence and leadership.
They rebounded last season while leading the Pacific Division for most of the year and returning to the playoffs, but Brown managed just one assist in five postseason games while Los Angeles was bounced by San Jose in the first round.
With no playoff series victories in two years and an aging core still near its prime, Lombardi apparently felt a leadership change was necessary for the Kings to return to championship contention.
The Kings' future is strongly tied to Kopitar, the sublime two-way center whose steady play exemplifies the Kings' style in Sutter's tenure. Sutter recently agreed to a contract to return to the Kings this fall for his sixth season and beyond.
Star defenseman Drew Doughty also is expected to take a more prominent leadership role for the Kings this fall, likely assuming an assistant captaincy.
Brown's future is more questionable with the Kings, and Lombardi's decision to take away the "C" makes it even more tenuous.