Iribar made his senior debut for Athletic in 1962 and his international debut in 1964. He was a member of the Athletic team that won the Copa del Generalísimo in 1969 and 1973 and reached the UEFA Cup final in 1977. In 1970 he also won the Zamora Trophy. He made a record 466 appearances in La Liga and a further 49 appearances for Spain. This included three games at the 1966 World Cup. He was also a member of Spanish team that won the European Championship in 1964.He still has the record for keeping a clean sheet at ten successive home games, or 1,018 minutes, during the 1970-71 season.
On 5 December 1975, before a game against Real Sociedad, Iribar and the captain of Real Sociedad, Ignacio Kortabarria, carried out the Ikurriña, the Basque flag and placed it ceremonially on the centre-circle.
This was the first public display of the flag since the death of Franco. He subsequently became involved in Basque local politics and was a founding member of the independentist coalition Herri Batasuna. He is regarded as one of the finest Spanish goalkeepers ever.
In 1980 Iribar retired as a player and joined the Athletic coaching staff. In 1983/84 he coached Bilbao Athletic, the clubs reserve side, to second place in the Segunda División, their highest ever league position. He managed the first team for the 1986/87 season. He has been manager of the Basque Country national football team since 1988.