Peiró was born in Madrid. He played Atlético Madrid, where he would start and end his professional career. For Atlético, he played 166 La Liga games and scored 95 goals, over eight seasons. He moved to played for Italian clubs Torino, Inter Milan and Roma. He won a number of honours with Inter, including two Serie A titles and a European Cup in 1965. He played for the Spanish national team in two FIFA World Cups.