Lee was drafted in as right-hand man in the Sam Allardyce regime, which lasted only one match and 67 days before a newspaper sting operation cost the latter his job.
Southgate retained Lee’s services during his four-game interim spell but, having secured a four-year contract, is now looking for fresh ideas. Lee is the second Allardyce appointee, after Leicester coach Craig Shakespeare, to be moved on by the former Middlesbrough boss.
The future of a third, goalkeeping coach Martyn Margetson, is yet to be confirmed.
Announcing the departure, which had been expected, Southgate thanked the 57-year-old for his assistance in preparing the squad for games against Malta, Slovenia, Scotland and Spain.
“I have great respect for Sammy,” said Southgate. “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.
“I was grateful with the way he helped to steady the ship throughout October and November and we wish him well for the future.”
Lee, who previously worked with England during Sven Goran Eriksson’s reign, said: “I should like to place on record my sincere thanks to the FA for the opportunity they gave me to work with the national team. It has been a great honour.
“I should also like to thank the players and staff for their support during this period of my career and wish them all the very best for the future.
“In particular I wish Gareth and his new coaching team every success in the future.”
Southgate wants Chelsea’s Steve Holland to be his full-time No 2, though that is complicated somewhat by the Blues’ Premier League title bid.
Holland has worked alongside Southgate at Under-21 and senior level on a job-split basis, but is understood to favour a permanent role with the national side.
Whether that comes soon or at the end of the campaign remains to be seen, but it is clear that at least one of the three parties will need to compromise.