A five-time NBA champion with the Los Angeles Lakers during his playing career, Fisher takes over from Mike Woodson, who was fired in April after the Knicks missed the playoffs.
Fisher, 39, will shift from playing for Oklahoma City to steering a Knicks team that was 37-45 and missed the playoffs for the first time in four years.
Jackson, a former Knicks player who won a record 11 NBA titles as coach of the Chicago Bulls and the Lakers, was hired in March to turn the team around and wiped the slate clean by firing Woodson and his staff when the season ended.
The Knicks last won an NBA title in 1973, when Jackson played for the New York team as a defensive minded forward.
(Reporting by Larry Fine; Editing by Julian Linden)