It will be England's first meeting with Germany since the 2010 World Cup knockout round match in Bloemfontein, which Fabio Capello's men lost 4-1, but only after Frank Lampard had what would have been an equalising goal disallowed.
The Germany game will take place on Tuesday, November 19. Germany were the second visitors to the new Wembley in August 2007 and the fixture will be the final match of the FA's 150th anniversary year.
Four days earlier, on Friday, November 15, Chile will provide the non-European opposition Hodgson had been hoping for.
With a match against Argentina falling through and Uruguay unavailable as they must face Jordan in a World Cup play-off match, the FA have booked Chile for their first visit since 1998, when two Marcelo Salas goals gave them victory.
Chile completed a successful World Cup qualifying campaign with a 2-1 win over Ecuador to reach the Finals for the ninth time.
Claudio Borghi's most recent squad included three UK-based players, Cardiff defender Gary Medel, Gonzalo Jara of Nottingham Forest and Wigan's Jean Beausejour.