Southgate is leaving his post as the FA's head of elite development and has said he no longer wishes to be considered for the role of technical director.
Southgate, who will continue to work as a television pundit, said in a statement: "I'd like to place on record just how much I've enjoyed working at the FA over the past 18 months. It really has been an honour and a pleasure."
FA general secretary Alex Horne admitted his disappointment at Southgate's decision. Horne said: "Gareth has made an outstanding contribution in supporting Sir Trevor Brooking and myself across various aspects of our football development work over the last 18 months.
"We're disappointed, but understand his decision and would like to thank Gareth for his efforts and wish him well for the future.
"We continue to recruit for key technical positions within the FA at what is a very important and exciting time for the organisation, with the imminent opening of our new training centre at St George's Park."
Southgate played a leading role in bringing in significant changes to youth football, with smaller pitches, goals and team sizes until players reach the age of 13.
He added: "Hopefully, I have been able to play some part in delivering important changes to the way children play at the youngest levels. It has also been a tremendous experience to work on the delivery of St George's Park.
"The FA is heading in the right direction in terms of developing more, better coaches and players at all levels of the game under the leadership of David Bernstein, Alex Horne and Sir Trevor Brooking.
"I would like to thank them for their support throughout my time with the organisation. I've advised the FA that I will be pleased to help with specific projects moving forward."