Keene was born in the London area, and at the age of 20 became Surveyor to the Dean and Chapter of Westminster. Six years later, he was appointed Surveyor to the Fabric of Westminster Abbey. He worked in Ireland at various times between 1752 and 1766, but nearly all his known surviving buildings are in England, especially in London and Oxford, where he had houses, and on various country estates. While much of his work is in the neo-classical style, he was an early exponent of Strawberry Hill Gothic, making good use of his knowledge of the Gothic details of Westminster Abbey.
He died at his country house at Drayton Green near Ealing.