Celtic paid £3m to land the 24-year-old on a four-year deal from Schalke, but he scored just seven goals in 34 appearances last season and opted to move to Denmark when he was made a bit-part player by manager Ronny Deila.
Pukki made it clear he wasn't impressed with the one-horse-race Scottish top flight. "I am looking forward very much to playing in the Super League," he said.
"The competition is extremely fierce in this league, unlike in Scotland where there is only one good team . . . Celtic. When I heard of Brondby's interest, I called their keeper, Lukas Hradecky, who I know very well from the Finland squad.
"As a striker, I love to score goals, and I hope I can help the team by scoring some goals here."