The fixture, arranged as part of the agreement which saw the teams meet in Copenhagen in February 2011, will assist in manager Roy Hodgson's preparations for next summer's World Cup finals.
The Three Lions will face Chile and Germany next month in their final fixtures of what has developed into a successful 2013.
England's 2-0 win over Poland last week meant Hodgson's men secured a place in Brazil as winners of Group H.
Denmark came second in Group B but missed out on a play-off berth as they finished with the weakest record of the nine runners-up.
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- Roy Hodgson