Dirk Bender was carrying four of the large iguanas wrapped in canvas in a package when officials stopped him leaving the country.
He was convicted "of having altered the local ecosystem of the archipelago," park authorities said.
The Galapagos National Park has requested the Ecuadorian court give Bender the maximum four-year jail term. He should be sentenced in the coming days.
Bender was arrested at the airport on Baltra Island on July 8 after park officials noticed him carrying a suspicious package, which was found to contain four lizards wrapped in canvas.
The hidden reptiles were Galapagos Land Iguanas (conolophus subcristatus), which the International Union for Conservation of Nature ranks as "vulnerable" on its Red List of Threatened Species.
In 1976, wild dogs wiped out a colony of around 500 of the iguanas on the island of Santa Cruz. The national park rescued around 60 survivors and launched a captive breeding program to try to revive the species.
The yellowish lizards can grow to be over a metre long, with males weighing up to 13 kilos.
The iguanas have been seen to raise themselves off the ground to allow finches to eat ticks off their bellies -- the same Galapagos finches which inspired Charles Darwin when he visited the islands in the 19th century.
The Galapagos Islands, situated about 1,000 kilometres off Ecuador's coast, gained fame when Darwin visited in 1835 to conduct research and collect samples on which he based his revolutionary theories on evolution.
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The archipelago has been a UNESCO World Heritage Site since 1978 for the rich plant and animal life found both on land and in the surrounding ocean.