Veras, a second baseman, originally signed an amateur free agent contract with the New York Mets in 1989. After the 1994 season ended, he was traded to the Marlins for Carl Everett. He made his Major League debut with the Marlins in 1995.
In his rookie season, Veras finished third in the NL Rookie of the Year balloting. He led the Major Leagues with 56 stolen bases while hitting .261 in only 124 games. He also walked 80 times against only 68 strikeouts in 538 plate appearances, resulting in a very respectable .384 OBP.
In his second season with the Marlins, Veras had only stolen six bases in 12 attempts over 34 games while hitting .241. He went on the disabled list on May 10th with a hamstring injury, putting him out for six weeks. When he returned in June, he still was not displaying the speed which had allowed him to win the stolen base crown just one year before. He stole two bases in four attempts through his next 39 games, hitting .262 before a demotion sent him to Triple-A affiliate Charlotte in August. He would remain there through the end of the season.
In the offseason, Veras was traded to the San Diego Padres for Dustin Hermanson. He later also payed for the Atlanta Braves.
He finished his Marlins career with a .258 average and 64 stolen bases. He also walked 131 times against 110 strikeouts, resulting in an OBP of .383 for the Fish.
He is currently a roving coach for the Kansas City Royals.