At least as far as West Germany goes, it was allowed after the passage of a law that went into effect in 1957 - The Gesetz über Titel, Orden und Ehrenzeichen ("Law regarding Titles, Medals and Decorations"). It allowed awards that predated the Nazis taking over the government in 1933, as long as they were worn in their original form. Medals that were awarded from 1939 to 1945 could generally be worn, if overt Nazi party symbolism (swastikas, SS runes, and so forth) was removed. Medals awarded by other Axis powers required specific dispensation before they could be worn. The law applied both to veterans who may have wanted to wear the medals at reunions or whatnot, and to WWII veterans serving in the Bundeswehr.

Edit: Caught an error.