"You are a lucky son of a b****," a voice can be heard telling Konrad as he sat huddled in a police car in Palm Beach, Florida, shivering under a blanket with the heat cranked all the way up in the early hours of Jan. 8.
One official offers Konrad a seat in a vehicle as the other offers to look for another blanket.
"How far out were you?" one voice asks.
"About 10 miles," Konrad says. "I've been swimming since 1 o'clock."
"One o'clock in the afternoon?" the voice asks in disbelief.
"What time is it now?" Konrad asks.
"Like almost 5 o'clock in the morning," the voice responds.
"Shut the **** up," Konrad says with shock in his voice.
After asking for water, Konrad asks, "Is there any chance you have a phone ... to just let my family know I'm alive?"
Konrad dictates a number and a police officer can be heard telling Konrad's mother, "He's OK. He's a little cold and wet. He was in the water for a while but he's fine and we have the medics looking at him now."
The police video was obtained by radio personality Andy Slater of WINZ in Miami and confirmed as authentic by a Palm Beach Police spokesman.
Konrad later recounted his ordeal for the media, saying he "prayed to God" after falling from his 38-foot boat as he was trying to reel in a fish just as a large wave hit.
"I shouldn't be here," Konrad told reporters.
He described the frustration of seeing Coast Guard helicopters that didn't spot him. He faced darkness, 10-foot waves and 25-mile-per-hour winds while his boat moved away on autopilot. Despite being bitten by jellyfish and seeing a shark circle him, he kept swimming.
Once he reached shore, he said it was "bittersweet" because he couldn't walk.
"I had hypothermia and my body was shaking uncontrollably. I didn't realize it was five in the morning," he said.
ABC News' Susanna Kim contributed to this report.