Per Emil Wikoeren, head of the Customs Region - Southern Norway, said the man, posing as an asylum seeker, had swallowed the cocaine in 160 small packages.
"That is a Norwegian record and we have found nothing in our databases to indicate that anywhere in this world has anyone swallowed 3.5 pounds," he told state radio network NRK.
The man, originally from Nigeria and in his 20s, arrived from Madrid at the small airport near the southern Norway city of Kristiansand in late May.
Wikoeren declined to estimate the value of the cocaine. The customs service withheld information about the find until now to protect the investigation.
"There were things that resulted in us becoming interested and the longer we continued the more sure we were that something was wrong," he said.
The suspect, whose name was withheld in keeping with Norwegian practice, declined food or water while he was being questioned.
"That further strengthened our suspicions," he said. "We also know this smuggling method is often used when traveling by air."
When the man was X-rayed, hospital personnel were stunned by the images showing bags of cocaine in his stomach. It took three days before they all passed safely out of him and were recovered.
""It was a terrible risk. If any of these packages had leaked it would have resulted in death," said Wikoeren. "He said he spent hours swallowing the packages."
Wikoeren said the man's asylum request was denied and he's being held a refugee center near Kristiansand, 150 miles south of Oslo, while police investigate the case.