Sarah Shourd and Shane Bauer became engaged in January 2010 while being held in Evin Prison in Tehran, according to family friend and attorney Ben Rosenfeld.
The two were living in Damascus, Syria, in July 2009 when they visited the Kurdish controlled region of northern Iraq near the Iranian border. They were arrested by an armed Iranian border patrol near a popular waterfall, along with their friend Josh Fattal.
Iran accused all three of them of espionage, while the trio said they were only hiking in the area.
Iranian officials released Shourd in September 2010 because she was in poor health. Shourd did not return to Iran for a trial.
Bauer and Fattal were sentenced to eight years in prison, but were later released in September 2011.
The location of Shourd and Bauer's wedding is being kept private, Rosenfeld said. Fattal will serve as best man.
Since her release, Shourd has written about the psychological effects of solitary confinement, and argued against its use in the United States.
"Now that this day has come, all I can do is close my eyes and fill with gratitude, for our freedom, for the love of so many generous people around the world, and for the very soil under my feet," Shourd said in a statement.