Born in Madrid, Velázquez spent all of his 12 years in La Liga with Real Madrid. After three seasons on loan, to Rayo Vallecano and CD Málaga, helping the latter promote from Segunda División in 1965, he went on to appear in 402 competitive games for his main club whilst scoring 59 goals, winning six national championships, three Copa del Rey trophies and the 1965–66 edition of the European Cup, where he was featured in the final against FK Partizan.