He has replaced Jean-Yves Charlier, who announced in July he was to leave the business to explore "a new direction in his career".
Marshall has more than 30 years of experience in high technology and educational businesses, including Apple and Oracle.
He joined the company in April 2011 and was previously president of its North American business.
In July, Promethean World revealed revenue had dropped 22 per cent to £83.2m in the six months to 30 June 2012. It also recorded a massive loss before tax of £148m.
The dramatic fall was caused by a non-cash goodwill impairment charge of £140.5m.
Promethean World makes interactive tools, displays and systems for use in classrooms.