The 20-year-old, who can play in defence and midfield, has agreed a two-and-a-half year contract and could make his debut against Bristol City at Griffin Park on Tuesday night.
Yennaris made four appearances for the Gunners, including one as a half-time substitute against Manchester United in the Premier League in 2012.
Bees boss Mark Warburton told the club website: "Nico is a player we have watched for many years as he has come through the Academy at Arsenal.
"He is a very talented player, technically good and physically sound. He has a real tactical astuteness for a young player.
"Nico has shown great flexibility in terms of positioning, appearing for Arsenal at right-back, left-back and in midfield.
"Nico is in the same age category as George Saville, Jake Bidwell and Marcello Trotta.
"He is a talented young player and I am sure he will have a bright future at Brentford Football Club. We are delighted to secure him permanently."