Vibe has been a regular scorer in the Danish and Swedish leagues, with his three seasons at IFK seeing him score 45 goals in 76 appearances in all competitions.
The 28-year-old, who has been capped nine times by his country, has signed a three-year deal with the Sky Bet Championship club and could make his debut against Stoke City in a pre-season friendly at Griffin Park on Saturday.
Coach Marinus Dijkhuizen said: “I am very happy that we have been able to sign two attackers. We were short of numbers in that position.
“Lasse Vibe brings a lot of experience to our young squad. He can play in all positions in the front line and scored a lot of goals last season.
“I’m excited by the possibility to work with Lasse in training and look forward to seeing him in our team in the coming season.”
Vibe is the second attacking signing made by Brentford in the last 24 hours, following in the wake of Germany Under-21 international Philipp Hofmann who joined from Kaiserslautern on Thursday.