Jurist. Born at Saltoun Hall, the son of Henry Fletcher of Saltoun and nephew of another Andrew Fletcher (1655 - 1716), he was admitted to the Bar in 1717. Fletcher was appointed a Senator of the College of Justice in 1724 as Lord Milton, and a Lord of Justiciary in 1726. Serving as Lord Justice Clerk between 1735 and 1746, he was praised for his measured application of the law in the wake of the 1745 Jacobite Rebellion. He was a close confidant and political agent of Archibald Campbell, 3rd Duke of Argyll (1682 - 1761).
Fletcher inherited Saltoun, and used part of the estate as a bleachfield c.1750 - he was founder and first Deputy Governor of the British Linen Company. He maintained Brunstane House as his Edinburgh home between 1747 and his death.