Sir Anthony Browne was the son of Sir Anthony Browne and Lady Lucy Neville, daughter of John Neville, 1st Marquess of Montagu and widow of Sir Thomas Fitzwilliam.

In 1518 he was appointed surveyor and master of hunting for the Yorkshire castles and Lordships of Hatfield, Thorne, and Conisbrough. He was included in the embassy to hand over Tournai to Francois I and Thomas Howard, Earl of Surrey, knighted him on 1 July 1522. In 1525 he was made lieutenant of the Isle of Man and in 1527 he became ambassador to France. In 1538 he received from Henry VIII, in recognition of his services the "house and suite of the late monastery of Battle" and in 1539 he was appointed Master of the Horse for life. He was made Knight of the Garter in 1540 and returned as knight of the shire for Surrey in 1539, 1542, 1545 and 1549.

Sir Anthony married twice. First, in 1528, to Alice, daughter of Sir John Gage by whom he had seven sons and three daughters. After Lady Browne died in 1540, he married Elizabeth Fitzgerald, daughter of Gerald FitzGerald, 9th Earl of Kildare and they had two two who died young. Elizabeth was one of the great beauties of the Court, known as "the fair Geraldine".

Sir Anthony died on 6 May 1548 at Byfleet, Surrey, and his body was wrapped in lead and buried at Battle in a tomb with his first wife. He was succeeded by his eldest son, Anthony.