Lampard, who will get his 84th cap for his country, has been given the armband after regular captain Rio Ferdinand was ruled out with a groin injury suffered ahead of Manchester United's game with Wolves on Saturday.
Steven Gerrard would have been favourite to replace Ferdinand but will also miss the game due to injury despite playing 90 minutes of Liverpool's win over Chelsea on Sunday.
England coach Fabio Capello said: ''I spoke with him [Lampard] about his injury that he suffered and I have been monitoring him during the last five games that he played. He has improved a lot. I saw him play against Liverpool and thought that he had a really good game - probably he is fresher than the other players.''
The 32-year-old will captain a somewhat depleted Three Lions side in Denmark, but said it would be a huge honour.
"I am very proud, it is quite unexpected," said Lampard. "I've been in the squad for a long time time now and I've go to a point where I am one of the old stagers. It will be one of the proudest moments of my career.
''I did have it [the armband] in the second half against Austria, under Steve McClaren and I was very proud then, but to actually walk out as captain is a huge deal. It's one of those things that, as a kid, you grow up dreaming about.
''I will try and do what I do for Chelsea. I won't change my character because of the armband. I want to be an example in the way that I play and talk to the players around me and hopefully that will have a strong influence on the team.
''The side certainly has other leaders, as we know. But I will just try and do my usual job and have an influence on the team.''
Capello confirmed that Ashley Cole would start, making him England's most capped full-back, while Arsenal midfielder Jack Wilshere will play in midfield. Aston Villa's record signing Darren Bent will start the game up front, having impressed the Italian after his January transfer.
''I have watched two games he [Bent] has played for Aston Villa,'' Capello said. ''When he was with Sunderland he played a different style because the manager asked him to stay close to the box and be fresh to score goals, but now he runs a lot more, presses a lot because the team play with a different style.
''He played well before but if you want to play with the seniors at this moment you have to be good when you go forward but also when you have to win the ball back and I think he has improved a lot.''