The Danes edged the Republic of Ireland in qualifying for the continent-wide tournament and will visit Wembley on March 31 in the second of two friendlies at the national stadium.
The first match, against yet-to-be-confirmed opponents, will take place four days earlier in a match dedicated to the Heads Up mental health campaign fronted by the Duke of Cambridge.
The recent policy of taking the team outside of London will then continue in June, following road trips to Sunderland, Manchester City, Leeds, Leicester and Southampton over the past four years, although details of the venue and opposition have yet to be finalised.
The Football Association has also announced that one further away game will be staged within Europe.
England finished their Group A qualifying campaign on a high over the past week, running in 11 unanswered goals against Montenegro and Kosovo to finish of 27 points from eight games with a positive goal difference of 31.
That guaranteed them three group matches at Wembley during the finals, which are being hosted by 12 different cities.
The group draw will take place in Bucharest on November 30.