Strauss, twice an Ashes-winning skipper, was the overwhelming favourite to land the post of England director of cricket, a job created by the ECB last month following Paul Downton's sacking as managing director.
ECB chief executive Tom Harrison, who led the recruitment process, said in a statement: "Andrew's breadth of ideas, his passion for England cricket and his proven leadership skills shone out.
"He was an exceptional England captain, is an authoritative voice on the modern game and has a wealth of experience building successful teams.