Bauer, Shourd and Josh Fattal, all University of California, Berkeley graduates, were arrested in July 2009 and held in Iran on spying charges.
Bauer and Fattal were convicted and held for more than two years. Shourd was released after 14 months on bail.
All three say they were innocent of spying and had simply strayed across the countries' border while in the mountainous region.
Bauer proposed to Shourd while in prison, fashioning an impromptu ring out of threads from his shirt. Fattal served as the couple's best man.