Velez signed with the New York Yankees as an amateur free agent on December 23, 1969, and worked his way through their minor league system and made his Major League Baseball debut with the team on September 4, 1973, where he recorded his first hit off Detroit Tigers pitcher Mickey Lolich. Velez hit his first career home run on September 23 off Dick Tidrow of the Cleveland Indians in the second inning, then hit another home run in his next at-bat against Tidrow in the fourth inning to lead the Yankees to a 9–1 victory over Cleveland. Velez finished the season hitting .195 with 2 HR and 7 RBI in 23 games with the Yankees.