Financial details were not revealed but British and German media reported Brentford paid the release clause of 13 million euros ($14.31 million) with the player expected to replace David Raya in goal.
Flekken, who has been called up for the Netherland's Nations League finals, led the Bundesliga with 13 clean sheets in 34 matches this season as Freiburg finished fifth.
"He's a player with a lot of quality... He has big experience and joins us after two great seasons with Freiburg, who have just had a top season in the Bundesliga, finishing fifth and qualifying for the Europa League," coach Thomas Frank said.
"He was a big part of the team there and now he's coming to us and will hopefully make the group better and the team better. He's a very good shot-stopper and comfortable with the ball at his feet. His distribution is very impressive."
Brentford finished ninth in their second Premier League campaign under Frank.