The Irishman, who guided Brentford to wins over Manchester United and Liverpool this season, has the Bees sitting seventh in the Premier League and eyeing European qualification for the first time in their history. Andrews, 45, said he felt he needed to "earn my stripes" after following Frank's successful seven-year tenure.
"When Keith accepted the job last summer, he signed a three-year contract, but the intention was always that we'd review this at the earliest opportunity," said Brentford director of football Phil Giles. "Given our progress this season, I'm really happy that we have agreed this extension within the first nine months." Brentford return to Premier League action on Saturday when they host Burnley.