The 47 year has returned to the game after leaving his role as Shelbourne manager last year.
After recent discussion, reports have stated Andrews has moved Duff to the London club.
This is not the first time the pair has worked together, as they were both chosen by Republic of Ireland manager Stephen Kenny and brought into his coaching team in April 2020.
"I've known Damien for a long time, I’ve seen him up close throughout his coaching journey. We’ve been on courses together and worked together as coaches with the Republic of Ireland national team," Andrews said.
"Damien will bring experience, presence and a real level of detail to our coaching department. He will add to the great group we already have and I’m very pleased that he is joining us," he continued.
Speaking of his visit to the Brentford club, Duff said: "You look at maybe a couple of my ex-clubs, Blackburn and Chelsea, they’re two basket cases and that’s why they are where they are. Brentford, brilliant from top to bottom."
Duff first got a chance to coach back in 2017 where he coached Shamrock Rovers, taking charge of the club’s Under-15 side.
Celtic manager Neil Lennon then brought him to Parkhead in 2019, "The next best thing when you finish is obviously coaching and the next best thing for me, I didn't play for Celtic, but to come and coach here is top class," he said at the time.
