It is understood that the former Dundee United manager has agreed to succeed Gary Holt, who elected to move to Norwich City earlier this month.
Applications closed on Monday, with Houston the leading name to take charge. Former Hearts head coach Gary Locke and erstwhile Falkirk midfielder Russell Latapy were also linked with the post.
The appointment of Houston will bring an end to his role as a scout with Celtic and herald a return to frontline management for the first time in over a year. The 55-year-old - who spent three years with Falkirk as a player - left United by mutual agreement in January last year, having voiced concerns over the size of the club's playing budget.