The Irishman replaced Thomas Frank in June and has guided the Bees to seventh place in the Premier League, with the club now eyeing European qualification for the first time in their history. Andrews previously served as set-piece coach before stepping up to the top role at Brentford.
Club director Phil Giles praised Andrews as a 'really good fit' after an 'outstanding' first season, with the extension coming within just nine months of him taking the job.