The 55-year-old Chief Constable Marshall is presently the Chief Executive of the 'College of Policing', which is the professional body for police in England and Wales.
He will join the International Cricket Council in September.
"I am a life-long cricket fan and am very keen to play my part in keeping my favourite sport clean. My police career has taught me the importance of prevention and education, operating to clear standards, making best use of intelligence and prosecuting where appropriate," said Marshall.
Marshall began his career as a police officer in 1980. He was appointed Chief Constable of Hampshire in 2008, and was selected to head the new College of Policing when it was created in 2012.
He holds a Masters Degree in Criminology from the University of Cambridge and also attended the Royal College of Defence Studies.
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