Grella, 24, joined Leeds in 2009 and spent time there and on loan at Carlisle United and Swindon Town.
According to Brentford, Grella and Leeds “reached a mutual termination agreement” to allow the former Duke Blue Devil to join the Bees.
Grella grew up on Long Island, N.Y., and was called up to junior U.S. national teams but never has represented his country at the senior level. He spent the 2010-11 season on loan at Carlisle and Swindon, scoring a combined four goals.
Brentford said Grella will be available to play in Saturday’s game against Tranmere Rovers.