Henry was the fourth son of Henry, Baron Norreys of Rycote, and his wife, Margery the daughter of John, Lord Williams. He matriculated at Magdalen College, Oxford, in 1571, and was created MA in 1588. He was captain of a company of English volunteers at Antwerp in June 1583, and while serving with his brothers, John and Edward, in the Low Countries in September 1586 was knighted by the Earl of Leicester after the Battle of Zutphen. He was sent to Brittany in May 1592 to report on the condition of the English forces and, in December 1593, was captain of a Regiment of nine hundred Englishmen there. He was MP for Berkshire in 1589 and 1598, but spent his latest years with his brothers, John and Thomas, in Ireland. In 1596, he was Colonel-General of Infantry. Taking part under Robert Devereux, 2nd Earl of Essex, in the campaign in Munster in June 1699, he was wounded in the leg in an engagement with the Irish at Finniterstown. He bore "amputation with extraordinary patience," but died a few weeks later.