 He was educated at Corpus Christi College, Cambridge, afterwards becoming a fellow of Jesus College in the same university.He was among the divines consulted about the legality of Henry VIII's marriage with Catherine of Aragon, became one of the royal chaplains about 1530, and became Bishop of Ely in 1534; he was consecrated a bishop on 19 April 1534, by Thomas Cranmer, Archbishop of Canterbury, assisted by John Longland, Bishop of Lincoln; and Christopher Lord, suffragan bishop of Canterbury and Bishop of Sidon.The diplomat Nicholas Hawkins had been the successor in waiting for his uncle Nicholas West; but he had recently died on a mission to Emperor Charles V.

Goodrich was favourable to the Reformation, helped in 1537 to draw up the "Institution of a Christian Man" (known as the "Bishops' Book"), and translated the Gospel of St John for the revised New Testament.