Hay, 21, joined the Bees in 2023 from Hitchin Town and spent the second-half of last season on-loan with Cheltenham Town.
New Brentford B manager Sam Saunders told the club's website: “We’re really pleased for him. He came into our environment from non-league and deserves a lot of credit for the way he applied himself every day.
"From the moment he signed, he showed a strong work ethic and commitment to improving, which earned him regular minutes and a good number of goals last season.
“After a positive loan spell in League Two last season, this feels like the perfect next step for him. Knowing the type of player and person Ash is, I am confident he will continue to learn and grow as a player.
"We wish him all the best - he’s worked hard for this opportunity and deserves every success.”