Holt was arrested in June 2016, after he had traveled to Venezuela to marry Thamy.
Holt's release comes more than a week after he posted videos to Facebook during a prison riot, pleading for help from Americans and the USA government. Holt had planned to spend several months in Caracas in the summer of 2016 with his new wife, Thamara Candelo, and her and her two daughters, to secure their visas so they could move with him to the U.S. Instead, the couple was arrested at her family's government housing complex on the outskirts of Caracas. Holt was held for almost two years without standing trial.
"We are grateful to all who participated in this miracle", Joshua Holt's family said in a statement.
Trump, in a tweet, did not identify Holt by name but Utah Senator Orrin Hatch confirmed that the Utah resident had been freed.
The United States accuses Maduro's government of stifling democracy, repressing the opposition and massive corruption.
Sen. Marco Rubio, R-Fla., who has Trump's ear on Latin America issues and spoke to Trump at length Friday night, said the couple's release "will in no way change US policy toward the dictatorship in Venezuela".
The video comes hours after Hatch announced he had secured Holt's release in a statement, calling the return of his fellow Utah native the culmination of two years of negotiations with the Venezuelan government and President Nicolas Maduro. "Senator Hatch has worked tirelessly on the Holt family's behalf, and I was honored to play a small role in bringing Josh and his wife home to the United States".