Spurs' ex-head of coaching and development will replace Les Reed, under whom he has served as assistant technical director since joining the FA in May.
McDermott was a highly-valued figure at Tottenham, where he spent 15 years and helped to develop several of the club's successful academy graduates including the likes of Harry Kane, Harry Winks, Danny Rose and Andros Townsend.
While he will make the step up in January 2021, the FA confirmed that Reed, 67, would continue to be involved in "external working groups, including as vice-chair of the Uefa Technical Development Committee and as a director of the Professional Game Academy Audit Board".
FA chief executive Mark Bullingham said: “Les has led the technical division, the largest team we have, through an extremely difficult period for all caused by the global pandemic. He and his team have taken tough decisions to react positively to these challenges.
"He has restructured and redistributed resources in a way that protects our development pathways, focusing activity to give us the best possible competitive advantage.
"Les offers high-level counsel on almost any issue and will be missed but has put in place a strong successor in John McDermott.
"I am delighted John has agreed to step up and have complete confidence in him to continue to take the technical team forward while helping our England teams to achieve success."