The 20-year-old, who can also play in defence, has penned a two-and-a-half-year deal with the Bees.
"Nico is a player we have watched for many years as he has come through the academy at Arsenal," Brentford boss Mark Warburton told the club's official website.
"He is a very talented player, technically good and physically sound. He has a real tactical astuteness for a young player."
Yennaris could make his Brentford debut on Tuesday when they host Bristol City in League One.