Ferrabosco was born at Greenwich, the illegitimate son of the Italian composer Alfonso Ferrabosco the elder. His mother might have been Susanna Symons, whom Alfonso the elder later married. Ferrabosco the younger was left under the guardianship of Gomer van Awsterwyke, a member of Queen Elizabeth I's court. Although Alfonso the elder asked for Alfonso the younger to be sent to him in Italy, where he had moved with his wife, the Queen insisted that he stay in England. Ferrabosco remained in Gomer van Awsterwyke's care until Awsterwyke's death in 1592. At this time he started a long career as a court musician, including as the private music tutor of Prince Henry.