The deal, which brings the four-times capped Flekken from Bundesliga side Freiburg, is subject to international clearance and work permit.
“We’re very happy to have signed Mark,” head coach Thomas Frank told the official Brentford website.
“He’s a player with a lot of quality who will strengthen our goalkeeper group.
“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.
“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.”
Flekken began his career in his native Netherlands at RKVV WDZ and Roda before moving to Germany, where he has played for Alemannia Aachen, Greuther Furth, Duisburg and Freiburg.
The 29-year-old made his Netherlands debut in March 2022 and kept 13 clean sheets in 34 Bundesliga matches – the highest tally in the division last season.
Frank has said Brentford goalkeeper David Raya could leave the club this summer after four successful seasons in West London.
But Frank warned interested parties that it will cost them £40million to sign the 27-year-old Spaniard.