After expressing her appreciation to the president and U.S. officials Holt's mother Laurie added: "I also want to say thank you to President Maduro for releasing Josh and letting him come home".
Holt's family says "we are grateful to all who participated in this miracle".
Holt's release comes as Maduro moves to ease tensions that have spiked since the May 20 elections, which were boycotted by most opposition parties and denounced as illegitimate by the US, EU, Canada and at least a dozen Latin American countries.
Holt, a 26-year-old Mormon missionary from Utah, had travelled to Venezuela in June 2016 to marry Caleno, whom he had met on the internet. Venezuela has held Holt and his wife on weapons charges without a trial since 2016.
"I'm just overwhelmed with gratitude", said an emotional Mr Holt, sitting next to Mr Trump in the Oval Office.
Saturday's outcome, Hatch said, resulted from work across two presidential administrations and with diplomatic contacts, ambassadors and Maduro himself.
"This type of gesture. allows us to consolidate what has always been our standpoint: dialogue, agreement, respect for our independence, respect for our sovereignty", Rodriguez said.
Joshua Holt arrived Saturday evening at Washington Dulles International Airport.
Holt said he was overwhelmed with gratitude for the support he received from the United States government while behind bars.
Following the vote, Maduro expelled USA charge d'affaires Todd Robinson and his deputy for allegedly conspiring to sabotage the vote by pressuring opposition parties to boycott the election, which had the lowest voter turnout in decades. "When you look back on your tenure during the presidency, this is just one of many great things you're doing, but it's really a great thing". Authorities accused him of stockpiling an assault rifle and grenades, and suggested that his case was linked to other unspecified US attempts to undermine Maduro's rule amid deep economic and political turbulence. "The United States will continue to use all available tools and options to pressure the Maduro regime to abide by democratic norms".
Hatch and Rep. Mia Love, R-Utah, also lobbied on behalf of Holt and decried his poor treatment in prison.
In a tweet, Trump referred to Joshua Holt as a "hostage". Hatch was officially notified Friday that Holt's release was being finalized, according to an official familiar with the events, and Corker had kept in close contact with Hatch, who had spoken several times with Maduro about Holt's situation.
In a harrowing recent Facebook post, Holt pleaded for help and for his life, from a Caracas jail.
Maduro was re-elected to a six-year term last week, but the USA joins other countries in rejecting the outcome, widely seen as a result of vote-rigging.