But the Bairns are three points adrift at the bottom of the Scottish Premier League table and lost 1-0 at home to Kilmarnock on Wednesday.
Former Falkirk player May had been on the coaching staff for five years.
May has been credited with a major role in the development of first-team players such as captain Darren Barr, Thomas Scobbie and Scott Arfield.
At the time of his appointment, May said he was relishing the prospect of "moving up to the next level".
But his debut season in the Falkirk dugout has proved difficult, with the Bairns losing 15 of their 27 games in all competitions, winning four and drawing eight.
Source: BBC Sport