Lee was brought in by Southgate's predecessor Sam Allardyce, whose tenure lasted just 67 days.
Former Liverpool midfielder Lee, 57, was brought in by Southgate's predecessor Sam Allardyce, whose tenure lasted just 67 days after he was brought down by a newspaper sting.
Lee worked alongside Southgate during the latter's four-game interim stint at the helm, but having now been awarded a four-year contract, Southgate will look to appoint his own assistant.
"I have great respect for Sammy," Southgate said in an FA press release.
"He is somebody who I worked with as a player and his personality and professionalism were excellent throughout my period as interim manager.
"I felt it was important for me to bring in my own support team and Sammy fully respected that."
Lee said it had been a "great honour" to work with England.
Southgate is reported to want Chelsea assistant coach Steve Holland to be his full-time number two.