The two spoke to The Associated Press on condition of anonymity because the team didn't immediately announce the hiring, which was first reported by KDCO-AM and FM Mile High Sports Radio in Denver.
Phillips, 67, interviewed for the position Tuesday.
He was Kubiak's defensive coordinator in Houston from 2011-13 and replaced him as interim coach when Kubiak was fired by the Texans in December 2013.
Phillips has also coached the Saints, Cowboys, Bills and Broncos, where he went 16-16 from 1993-94.
He was out of football last season for the first time since 1975.