Utah man Joshua Holt and his wife Thamy have been in a Venezuelan prison since 2016 after being arrested for firearm offences. Bob Corker, chairman of the Senate Foreign Relations Committee, and close allies of Maduro.
"The great people of Utah will be very happy", Trump wrote.
Hatch has been a devout supporter of Trump since he came into office
Venezuelan authorities arrested Holt in June 2016 while he was in Venezuela for his wedding, and he was held without trial at the headquarters of intelligence agency Sebin, a Caracas complex known as the Helicoide.
Holt's release looked unlikely a week ago, when he appeared in a clandestinely shot video railing against the Maduro government and saying his life was threatened in a prison riot.
The U.S. government at first avoided ratcheting up public pressure on Venezuela amid already strained relations between the two countries, but eventually raised Holt's case to the highest levels of the Venezuela government.
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In a statement on Facebook, Holt's family gave thanks "to all who participated in this miracle", but asked to be allowed to meet him and his wife before giving any further statements or interviews.
There has not been any official confirmation or comment from President Nicolás Maduro's government.
The video, posted on the Twitter account for Hatch's office, depicts Holt and his wife, Thamy, reuniting with family in the senator's Washington, D.C., office, with the caption "Reunited".
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In their statement, the Holt family said, "We thank you for your collaboration during this time of anguish".
The news of their release comes just days after Venezuela's presidential election. "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".
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The money, court filings said, came from her book and speaking engagements, soap making, doll making and artwork sales. She said in 2017 that while she might be "Caucasian biologically" she nevertheless "had an authentic black identity".
On May 17, Holt issued a plea on Facebook, asking the U.S. government to help him return home.