Vanterpool, 48, had been serving as associate head coach with the Timberwolves.
Meanwhile, the Nets have been looking to replace Ime Udoka, who left to become head coach of the Celtics.
Vanterpool first came to the NBA in 2012 following a playing and assistant coaching career with CSKA Moscow. He served as an assistant with the Trail Blazers from 2012-19 with former coach Terry Stotts, before signing on with the Timberwolves.
Vanterpool was passed over in the middle of the season for the head-coaching job, which eventually went to ex-Raptors assistant Chris Finch, and Wojnarowski reported in May that Vanterpool would be leaving Minnesota.