One fan made a Nazi salute, while the other mimicked an Adolf Hitler moustache with his finger and made a cut-throat gesture towards Germany fans.
The pair received the first lifetime bans every issued by the FA, officials told reporters at the St George's Park national football centre in Burton-on-Trent, central England.
The game in Dortmund, which Germany won 1-0, also led to 27 members of England's official travel club being temporarily banned from attending matches and six receiving written warnings.
"The behaviour of a section of the England support in Dortmund was inappropriate, disrespectful and disappointing," Clarke said at the time.
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"The FA has consistently urged supporters to show respect and not to chant songs that could be regarded as insulting to others.
"Individuals who engage in such behaviour do not represent the overwhelming majority of England fans, nor the values and identity we should aspire to as a football nation."
England were threatened with expulsion from last year's European Championship in France after running battles between English and Russian fans in Marseille.
Since 2014, 142 England fans have been issued with bans ranging from six months to five years, with 239 issued warnings.
The FA said 4,761 members of England's official supporters club would travel to Glasgow for Saturday's World Cup qualifier against Scotland, which is seen as having "potential for risk".