A right hook sent Magee down for a third and last time, after Kessler also floored the Northern Irishman twice in the second round.
"Magee came out quickly. But when he got the one in the stomach, I just hoped he wouldn't be able to storm out again," Kessler said about the first blow before a roaring and partisan crowd of more than 10,000 fans.
Kessler (46-2 with 35 knockouts) last held a world title in 2010, the WBC version.
In 2004, the Warrior Viking beat Manny Sica from Puerto Rico and grabbed the WBA title. Two years later, Kessler knocked out German Markus Beyer to get the WBC belt, and became WBA champ in 2008 with a victory over Dimitri Sartison of Germany. The Dane then took the WBA title with a victory over Britain's Carl Froch.
Kessler returned to the ring last year after overcoming an eye injury that forced him to withdraw from the Super Six tournament in 2010. The eye injury stemmed from a Super Six bout against American fighter Andre Ward in 2009.
Magee (36-5) lost his second defense of the WBA belt he won in July last year.
"I came here to fight but that first jab really hurt me a lot," Magee said.
He had traveled to Denmark hoping to complete a hat trick of wins over Danish opponents after