The former Czech Republic Under-21 captain will join up with the Bees on a year-long deal having already played under Uwe Rosler at Norwegian side Viking FK.
With three full international caps to his name, 27-year-old Fillo joined up with the Brentford squad at their training camp in Germany and new boss Rosler is already looking forward to working with him again.
"I know Martin from my time in Stavanger and I signed him for a big fee," the 44-year-old told the club's official website.
"He did very well for me, especially in his first year, and I look forward to seeing him play in our shirt and scoring goals.
"He will fit in with the squad as a player and as a person."