Anasagasti was born to exiled Spanish parents in Cumaná, Venezuela. His father was a Basque nationalist and a member of the Basque Nationalist Party (PNV), who had fled the country after the Spanish Civil War. In the mid 1950s, his parents decided that Iñaki and his three brothers had to be educated in the Basque Country of Spain, so sent their children to return to San Sebastián to the care of their grandparents. Iñaki studied at the Sociedad de María, San Sebastián from 1955 to 1961 and from this date to 1965 in Santiago Apóstol of Bilbao.