Utah Senator Orrin Hatch said in a statement that Holt's release followed two years of intense lobbying, working with two presidential administrations, countless diplomatic contacts around the world, and Maduro himself.
A secret backchannel led by a veteran Republican Senate staffer and a flamboyant Venezuelan official nicknamed "Dracula" broke through hostile relations between the two governments to secure the release of American prisoner Joshua Holt, who traveled to the South American country for love and ended up in jail, without a trial, for two years. President Donald Trump tweeted that it was "good news", adding that Holt "should be landing in D.C. this evening and be in the White House, with his family, at about 7:00 P.M".
Holt told Trump: "I'm just overwhelmed with gratitude", adding his imprisonment on weapons charges had been very hard and "not really the great vacation I was looking for".
Trump later hosted the family in the Oval Office and told Holt he was "brave" and "went through a lot". They planned to stay in the country long enough for Thamy to obtain a US visa.
They were welcomed to the White House by US President Donald Trump, who told Holt he had been "incredibly courageous".
Mr Holt was jailed and branded the CIA's top spy in Latin America after travelling to Venezuela from Utah in 2016 to marry Spanish-speaking Mormon Thamara Caleno in the country.
The Venezuelan government said Holt and his wife were freed in a goodwill gesture to the US, a measure that surprised some knowing the combative history between the two nations.
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Venezuela's chief spokesman, Communications Minister Jorge Rodrigues, said he hopes the release will engender "respect for our independence and respect for our sovereignty".
Trump asked everyone sitting with him in the Oval Office to speak about Holt's release but was surprised - and amused - when Lee turned to Holt's daughter to address her in Spanish.
"This wouldn't have happened without you", Hatch said.
The statement called for "new elections and the democratic process", the release of all political prisoners and the acceptance of "desperately needed worldwide humanitarian aid for Venezuela's dying citizens". Hatch issued a statement shortly after the president's first tweet. In June of that year, he was arrested by the government, which accused him - with the help of planted evidence, observers say - of stockpiling weapons as part of an American efforts to topple the government of President Nicolas Maduro. "They want to kill me and paint the walls with my blood".
Since his arrest, his mother, Laurie, worked to have her son freed from the prison, where she said he was being held on false charges and suffering from health problems.
"We thank you for your collaboration during this time of anguish", Holt's family said in a statement to The Associated Press on Saturday.
Earlier in May, Holt made a desperate Facebook plea for help after a riot at the prison where they were held.
In televised comments earlier this month, the No. 2 official in Venezuela's ruling Socialist Party, Diosdado Cabello, described Holt as "the head of USA espionage in Latin America" and said that he would remain behind bars. USA officials say the charges were trumped up.