Its time for change, and for a new chapter. Sundays final in Berlin against Spain was my final game as England manager, Southgate said in a statement.
Names immediately bandied around as 53-year-old Southgates successor are Newcastle manager Eddie Howe, and two former Chelsea handlers, Graham Potter and Mauricio Pochettino.
Football Association CEO Mark Bullingham said Southgate had made the impossible job possible.
Southgate took over in 2016 when Englands fortunes were at a low ebb, having exited the Euros after defeat to Iceland and then Sam Allardyce had to resign over a scandal.
In the last four tournaments Southgate led England to three semi-finals and two finals.
