The promotion of Andrews aligns with Brentford's policy of promoting from within, especially after former assistant Justin Cochrane also joined Frank at Spurs.
This marks his first managerial position, following a playing career and coaching roles with MK Dons and the Ireland national team.
Brentford's director of football, Phil Giles, praised Andrews as a very good fit who will bring evolution while maintaining the club's established playing style, despite potential player departures this summer.