He will replace Michael Grade who announced last April that he wished to give up the role.
Crozier is also a former boss of the Football Association.
He returned the Royal Mail to profitability but the service has been hit by strike action.
ITV chairman Archie Norman said: "ITV is a strong brand with talented people, facing an imperative for change as the media landscape evolves.
"Adam is a very strong leader with a great track record in delivering transformational change."
Crozier said ITV was "a company with great heritage and one of the best brands in the UK".
He added: "The entire media sector is going through enormous change and that presents both great opportunities and significant challenges for everyone in the industry.
"The objective for ITV is to rise to those challenges and put itself at the forefront of change. I am very much looking forward to working with the people at ITV and leading the transformation ahead."