VanGorder previously worked with Notre Dame coach Brian Kelly at Grand Valley State from 1989-91.
VanGorder is in his first year as linebackers coach with the Jets after serving as Auburn's defensive coordinator last season. The Tigers went 3-9 with his defense, including 0-8 in Southeastern Conference play.
His hiring was earlier reported by NFL Network.
Kelly said Saturday after Notre Dame's win in the New Era Pinstripe Bowl that the Irish have their new defensive coordinator in place, but he would not reveal the name because the contract has not been finalized.
An official announcement is expected shortly after the NFL regular season ends.
Information from ESPNNewYork.com contributor Matt Ehalt was used in this report.