The deal is for one season and partially guaranteed, per ESPN sources. Financial terms were not announced.
Vonleh, the No. 9 pick in the 2014 NBA draft, will compete for a rotation spot on New York's front line. He will have an opportunity to earn minutes at power forward with Kristaps Porzingis sidelined while rehabbing from ACL surgery.
Once Vonleh signs, New York will have 16 players under NBA contracts and two players under two-way contracts, so they will need to waive or trade a player before opening night to satisfy the NBA's roster limit.
The club also added former lottery pick Mario Hezonja earlier in free agency and now has nine former lottery picks on the roster.