Signed by the New York Mets as an amateur free agent in 1989,[1][2] Veras was named to the Triple-A All-Star Game while playing for the Norfolk Tides in 1994.[3] He was subsequently traded to the Florida Marlins for Carl Everett in November 1994,[4][5][6] and made the Marlins' Opening Day roster, debuting at the major league level on April 25, 1995.[7][8] In 1995, Veras' rookie season, he led Major League Baseball with 56 stolen bases. At the conclusion of the season, Veras ranked second behind Chuck Carr for the franchise record in stolen bases. He set single-season franchise records in walks (80), tripes (7), and runs scored (86). Veras tied the franchise record with nine hit-by-pitches, and led all major league rookies with a .384 on-base percentage.[9] During the 1996 season, Veras was injured on May 10, placed on the disabled list for a month and a half, and played in 43 major league games thereafter, eventually being sent to the Charlotte Knights.[9][10] On July 14, 1996, Veras made the final out in a no-hitter pitched by Ramón Martínez.[11][12]
On December 22, 1999, he was traded from the San Diego Padres to the Atlanta Braves along with Wally Joyner and Reggie Sanders, in exchange for Ryan Klesko, Bret Boone, and a minor leaguer.[20][21] In January 2000, the Braves and Veras avoided arbitration by agreeing to a one-year deal worth $3 million for the season.[1] He hit for a career-high .309 batting average for the Braves in 2000 before tearing his ACL in a game against the Baltimore Orioles on July 14, 2000.[22][23]
Veras returned to the Braves' lineup in 2001, but would be plagued with injuries in what would be his final season, eventually being designated for assignment by the Braves after suffering injuries to his rib cage and ankle.[24] He appeared in his final major league game on July 13, 2001. Veras subsequently signed a minor league contract with the Boston Red Sox in August 2001,[25] and participated in spring training with the team prior to the 2002 season.[26] In December 2002, Veras signed a minor league contract with the Los Angeles Dodgers.[27]
The Kansas City Royals hired Veras as a roving coach for the 2008 season,[28] and retained him as a bunting and baserunning coordinator the next year.[29] Veras returned to the Royals organization in 2018 as the bunting and baserunning coach for the Dominican Summer League Royals.[30] He remained in the position for the 2019 season.[31] Veras was not retained for the 2020 season,[32] but returned in the bunting and baserunning role for the 2021 season.[33] In 2022[34] and 2023,[35][36] Veras served as the bench coach.