Shirreff was the son of an East Lothian farmer. After spending his youth in the West Indies as a merchant, he returned at his father"s death, and succeeded to the lease of the farm at Captainhead, Haddington.
In 1793 he was chosen, together with two other East Lothian farmers to survey the West Riding of Yorkshire for the county agricultural reports of the Board of Agriculture. Shirreff attempted agricultural improvements, including a threshing-machine, worked by wind, and a bone-mill. He tried without success to introduce into Scotland the use of bone-dust as fertiliser.
After subletting his farm, he resided at Craigside, Abbey Hill, and other places in and around Edinburgh, writing on agricultural topics.
During the last years of his life Shirreff resided in the country, taking charge of the estates of some noblemen. He died 2 November 1818, and was interred in the burial-ground at Prestonkirk, East Lothian.