The Hungarian FA was given a three-match stadium ban after trouble at the Puskas Arena at Euro 2020.
England begin with away games against Germany and Hungary, and then the home games against Italy and Hungary, in June next year.
They then face Italy away and Germany at home in September, in games Southgate will use as part of his preparation for the winter World Cup in Qatar.
UEFA hit the FA with a two-match stadium ban, with one match suspended for two years, following trouble at the Euro 2020 Final at Wembley.
The FA was also hit with a fine of €100,000 (£85,000).
England Nations League fixtures in full:
Hungary vs EnglandJune 4, 2022
Germany vs England June 7, 2022
England vs Italy June 11, 2022
England vs Hungary, June 14, 2022
Italy vs England, September 23, 2022
England vs Germany, September 26, 2022.