Velarde was selected in the 19th round of the 1985 amateur draft by the Chicago White Sox. On May 29, 2000, Velarde turned an unassisted triple play for the A's versus the Yankees - just the 11th in Major League history. He appeared in the 2001 World Series as a member of the Yankees.
Velarde's name is mentioned several times in connection with steroids in the 2006 book Game of Shadows, which details the use of performance enhancing drugs in modern sports, in particular Barry Bonds and the BALCO scandal. It was revealed on December 13, 2007 in the report by Senator George Mitchell in the Mitchell Report that he had purchased steroids or other performance-enhancing drugs.
Currently, Velarde is retired and resides in his hometown of Midland, Texas.