The Bees have been without a permanent manager since Andy Scott was sacked in February with Nicky Forster taking over as interim boss for the remainder of the season.
Now they have secured Rosler on a two-year deal and the former Molde, Viking and Lillestrom boss was happy to have clinched the deal.
"I am delighted to have been appointed as manager of Brentford," he said.
"It has long been my desire to manage and coach an English league side and having spoken to senior representatives of Brentford it became obvious they share the same drive, ambition and vision to succeed.
"I'm excited at the prospect and can't wait to meet the players in preparation for the challenge ahead."