He joins general manager Scott Perry and assistant general manager Gerald Madkins in the new-look Knicks front office.
The news was first reported by Shams Charania of Yahoo!
Robinson had been with the Bucks since 2015.
With the Knicks, Robinson will fill roles including player development as well as serve as general manager for the Knicks' development league team in Westchester.
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Although Mills has not been team president for long, he is quickly making a break from the Jackson era, which lasted three years.
Robinson was head coach at Brown and Oregon State for a total of eight seasons, most recently in 2013-14.
The 55-year-old was a renowned player from 1979-83 at Princeton University, where he was a two-time Ivy League Player of the Year.
Robinson has previously worked for the Milwaukee Bucks as their vice president of player and organizational development. Robinson has coaching and executive experience on the college and professional levels.
According to Charania, Robinson's job will be multi-faceted, taking on various different responsibilities in NY.