Son of Patrick Agnew (d. 1758), 2nd of Dalreagle, and Mary Stewart. Married (1763) to Penelope Agnew, daughter of Sir Andrew Agnew (1687-1771), 5th Bart of Lochnaw.
Agnew graduated MA from Glasgow University in 1750 and he was admitted advocate in 1754. At his death on January 3rd, 1768 he was Judge-Advocate for North Britain, and Lt-Col in the army.
Boswell met Agnew at Kirroughtrie on October 2, 1762. He described him as "an agreeable little man enough". Boswell went to dine with Agnew and his family at Mertoun on the next day.