Velarde is best known for turning the eleventh unassisted triple play in Major League Baseball history on May 29, 2000.

He joined the New York Yankees in 1987, when the White Sox traded him with Pete Filson in exchange for Scott Nielsen and Mike Soper.

[4] Velarde made his debut in 1987, but spent the next two seasons dividing his playing time between the Class AAA Columbus Clippers of the International League and the Yankees.

[10] However, he was always considered a utility player[10] and subsequently reverted to the role, his versatility being cited as his main asset in contrast to his unreliable defense and lack of slugging prowess.

[3] He became a free agent at the end of the season for the first time in his career and re-signed with the Yankees for a one-year, $350,000 contract plus incentives, even though he was given a higher offer by other teams.

Though Velarde was keen to remain with the Yankees (the only team he had played for up to this point), they turned down his request for a three-year contract.

[8] He also became the sixth player in Major League history to amass 200 hits in a single season while playing for two different teams, and the first since Willie Montañez in 1976.

[12][13] In his second season with the Athletics, Velarde turned an unassisted triple play against the Yankees, his former team, on May 29 in the bottom of the 6th inning.

[17] He acknowledged that he had made a mistake when he departed the Yankees in 1995 in order to become an everyday player[13][18] and vowed to "redeem the part of the career [he] missed.