Scots-born Crozier, who stepped down from ITV in June, will join Vue with immediate effect.
Vue is owned by Canadian investors Omers and Alberta Investment Management Corporation and it is thought that Crozier’s appointment could pave the way for a potential sale or initial public offering.
As well as heading up ITV, he has been chief executive of Royal Mail, the Football Association and Saatchi & Saatchi.
The Canadian duo bought Vue for £935 million in 2013 from Doughty Hanson, but it is thought that any deal would now value the chain at more than £1.5 billion.
Crozier said: “I have watched the development and growth of Vue International with great interest and am excited to be joining the group to play an active role in furthering their future ambitions.
“They are uniquely positioned to entertain consumers, pioneering in the exhibition space and pushing for the best experience possible.”
Vue operates in ten countries across 212 sites.
Founder and chief executive Tim Richards said: “Adam is one of the most highly respected professionals in the UK with extensive experience across multiple industries.
“We look forward to benefiting from his invaluable perspective and insight to support our strategy and vision.”