The Three Lions faced Roberto Martinez’s Belgium side twice at the 2018 World Cup, once at the end of the group phase and again in the third-place play-off, losing on both occasions.
They are due to face the Danes in a friendly later this month – coronavirus permitting – while they famously lost to Iceland in Nice at Euro 2016.
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Wales and the Republic of Ireland will meet again after they were drawn in the same group.
Ryan Giggs’ men will take on the Irish in Group Four of League B in Uefa’s competition, which was a big success in its inaugural edition in 2018-19.
The sides met in that first competition too, with Wales winning both encounters.
The other sides in Group B4 are first-time Euro finalists Finland and Bulgaria.
Scotland, who are due to take on Israel in a Euro 2020 qualification play-off later this month, will also face them in the 2020-21 Nations League.
Steve Clarke’s men will also face the Czech Republic and Slovakia in Group B2.
Northern Ireland were drawn in Group B1 alongside Austria, Norway and Romania.
France and Croatia, who met in the 2018 World Cup final, were paired together in Group A3, while Spain and Germany go head to head in A4.
The group matches will be played between September and November this year.
The group winners from League A will contest the Nations League finals in June 2021, with one of them being selected to host it.
The competition also provides a back door to qualification for the 2022 World Cup.
The two highest-ranked Nations League group winners who do not either win their World Cup qualifying group or finish as runners-up will enter a 12-team play-off to secure the final three European places at the finals in Qatar.