The Hemel Hempstead boss has been chosen to replace Harry Wheeler, who left the club last month.
He leaves the Tudors after taking them to the National League South play-offs last season.
The Blues confirmed on their twitter account that Brennan will take training tonight and meet his players.
He will bring with him assistant Stuart Maynard, will also move the Essex club.
Brennan knows the division well and has taken Hemel to great heights after guiding the club up from the Southern League.
Owner Glenn Tamplin fired Wheeler after losing just one game - and was unsuccessful in getting him to return.
Billericay are up to second in the league, just two points off leaders Woking.