Sen. Marco Rubio, Florida Republican, who is considered to have Mr. Trump's ear on Latin American issues, said the couple's "release will in no way change USA policy towards the dictatorship in Venezuela".
Joshua Holt, 26, from Utah has been held in a Venezuelan prison on allegations of spying for the US, according to reports.
Holt had traveled to Venezuela to marry his then-partner Thamara Caleño, a native to the country, in 2016 before he was taken into custody by Venezuelan authorities. "The great people of Utah are Celebrating!" Bob Corker, chairman of the Senate Foreign Relations Committee, met with Venezuela's president, Nicolas Maduro, on Friday, two days after the embattled socialist leader kicked out the top US diplomat in the country.
USA authorities had been denied access to a court hearing on Holt's case in December, with Trump labelling the USA citizen a "hostage" of the Venezuela administration. In retaliation, socialist party boss Diosdado Cabello, a powerful ally of Maduro, said on state television that Holt was the CIA's top spy in Latin America.
The Trump administration has threatened crippling oil sanctions on Venezuela for Maduro's decision to go forward with the presidential election last week.
One woman interviewed by the Herald, said Holt had been framed with the crime because he was a US citizen, alleging that she and four other witnesses saw government authorities plant the weapons in Holt's apartment.
"We are grateful to all who participated in this miracle", Mr. Holt's family said in a statement.
"I'm pleased to announce that after two years of hard work, ew've secured the release of Josh and Thamy Holt, who are now on their way home to the United States from Venezuela".
Utah Senator Orrin Hatch posted video on Twitter of the pair being reunited with Holt's parents on Saturday evening, sharing hugs and tears. Maduro went forward with a presidential election last week that the USA has called a "sham".
The Maduro government has yet to comment on the reasons for the release.