Andrews, who replaced Thomas Frank, has guided Brentford to seventh place in the Premier League with notable wins over Manchester United and Liverpool. The former set-piece coach expressed his desire to prove himself following Frank's successful seven-year tenure.
"I really understood there would have been a slight concern," Andrews said. "I was always going to grasp the opportunity with both hands." Brentford director of football Phil Giles praised Andrews as a "really good fit" after an "outstanding" first season. The Bees host Burnley on Saturday.