Fizdale, 43, was New York's top target during its coaching search, according to the report.
According to ESPN Knicks reporter Ian Begley Fizdale and the Knicks have agreed to a four year deal.
Fizdale met with James Dolan on Thursday to finalize the deal.
Fizdale led the Grizzlies to the playoffs in his one full season as coach.
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That did little to diminish the respect of Fizdale, who had been an assistant to Erik Spoelstra in Miami when the Heat won two National Basketball Association championships and developed strong relationships with superstars LeBron James and Dwyane Wade. Fizdale was sacked after just 19 games the following season, one day after benching star center Marc Gasol. Since then the Knicks have won just one playoff series and become a perennial also-ran.
Some of the names included former hawks coach Mike Budenholzer and former Knicks head coach and current Clippers assistant Mike Woodson.
Fizdale had taken over in Memphis in May of 2016 and guided the Grizzlies to a 50-51 mark during his tenure. He coached the Knicks to a 60-104 record in two seasons. Fizdale was sacked the next day, though the Grizzlies said it was because of the team's overall performance, not the specific incident with Gasol.