The firm, which operates in 130 countries from 27 offices, helps organisations manage strategic and operational risks.
Its work covers political and security risk analysis, business ethics, anti-corruption services and crisis management. It has security contracts in Afghanistan and Iraq.
Cubitt won the account after a competitive pitch.
Control Risks previously used Monument PR out of the UK.
The account will be led by Cubitt founder Simon Brocklebank-Fowler and professional services partner Simon Barker, reporting to CEO Richard Fenning and comms director Georgina Parkes.
The brief includes strategic comms and media relations.