The 55-year-old American had a record of 454-304 while coaching the Cleveland Cavaliers, Los Angeles Lakers and Sacramento. The Kings dismissed him last December following a 13-18 start.
""After an extensive and thorough search process, we are excited to announce Mike Brown as the head coach of the New York Knicks," said Knicks president Leon Rose.
"Mike has coached at the highest levels in our sport and brings a championship background to our organization.
"His experience coaching in the NBA Finals, winning four championships as an assistant coach, and his ability to develop players will all contribute to our goal of bringing a championship to New York for our fans."
The Knicks, who have not secured an NBA title since 1973, reached the Eastern Conference finals for the first time since 2000 but were defeated by the Indiana Pacers.
This prompted the Knicks to part ways with Tom Thibodeau last month after five years in charge.
"Leon and our team conducted a comprehensive and thoughtful process that led us to Mike, and I am happy to see him on the sidelines for us next season," said Knicks owner James L. Dolan.
Brown had a record of 107-88 as the Kings' coach over three seasons. In the 2022-23 season, his first with Sacramento, Brown's team won 48 games and made the playoffs for the first time since 2006, earning him the NBA Coach of the Year award, the first to do so unanimously.
After serving as an assistant in Washington, San Antonio and Indiana - including a role on the 2003 San Antonio NBA championship team -- Brown became the Cavaliers' head coach in 2005, working with rising star LeBron James.
He guided the Cavs to the playoffs for the first time since 1998 and into the 2007 NBA Finals. He was named NBA Coach of the Year for the first time in 2010 after leading Cleveland to a league-best 66 wins.
He was let go in May 2010 as the Cavs prepared to welcome James back from his time in Miami. Brown took over as head coach of the Lakers one year later, only to be dismissed in November 2012.
Brown was rehired by the Cavaliers in 2013 but was again let go after they finished 33-49 and missed the playoffs.
From 2016 to 2022, Brown served as an assistant coach for the Golden State Warriors, who won three NBA championships during his tenure. In the 2017 playoffs, Brown went 12-0 while head coach Steve Kerr was unavailable during the Warriors' title run.
Brown moved to the Kings in 2022.