The former Dunfermline Athletic and Falkirk player was previously U23 coach at Sheffield Wednesday, where he also had spells as caretaker manager.
Bullen will be in the dug-out for Saturday's game against cinch Championship leaders Arbroath at Somerset Park.
Managing director Graeme Mathie told the club website: "In all our conversations with Lee, it became clear he had a great desire to be the first-team head coach at Ayr United and be part of the journey we want to start as a club.
"He brings a variety of experiences from his time playing and coaching in a number of different countries, and he has taken on a variety of leadership roles throughout his career."
