Cordero had an opportunity to make the Montreal Expos roster on Opening Day in 1992, less than four years after he signed with the team at the age of sixteen, but he struck out 17 times in 38 spring training at bats, and was sent down to Triple-A Indianapolis. He debuted with the Expos after the All-Star break and finished with a .314 batting average in 45 games, despite missing significant stretches of playing time due to a sprained ankle, a strained middle finger, and a serious case of chicken pox.

A line drive hitter, he finished his first full season with a .248 average, 10 homers and 58 RBIs in 1993. Meanwhile, he displayed excellent range at shortstop and a strong throwing arm. In the strike-shortened 1994 season, Cordero finished with a career-high .294 average, 15 home runs, 63 RBI, 65 runs scored and 35 doubles, and made the National League All-Star team. The next year he batted .286.

Cordero was traded to the Boston Red Sox before the 1996 season. The Expos received pitchers Rheal Cormier and Shayne Bennett, and first baseman Ryan McGuire in the deal. In his first year in Boston, a pair of nagging injuries and the presence of John Valentin at shortstop limited his playing time. Cordero was used at second base and as designated hitter, appearing in 59 games. His most productive season came in 1997, when he hit .281 and posted career-highs in home runs (18), RBI (72), runs (82), hits (160) and games (140). At the end of the 1997 season, the Red Sox released Cordero, and he signed with the Chicago White Sox.

In 1997, Cordero pleaded guilty to assault and battery against his former wife Ana. Later that year, a restraining order was issued against Cordero in Puerto Rico for his alleged threatening of his wife. In 1999, Cordero was arrested in New York and charged with disturbing the peace for an alleged altercation with his wife’s former husband. In 2002, Cordero was arrested in Orlando, Florida and charged with battery in a domestic violence case that was eventually dropped when the alleged victim refused to participate in the prosecution. During the 2000s Cordero made repeated attempts to reduce his court-ordered child support obligations.

From 1998 to 2004, Cordero played for five teams, including two stints with the Cleveland Indians and a full season with his former club, Montreal. In 2004, he had arthroscopic knee surgery and was out for the season. Cordero was back in 2005, with the renamed Washington Nationals franchise.

On July 25, 2005, the Nationals placed Cordero on waivers for the purpose of giving him his unconditional release. The 33-year-old Cordero, who had been bothered by knee problems, batted .118 with two RBI in 29 games that season for the Nationals. On July 27, the New York Mets signed Cordero to a minor league contract and assigned him to their Triple-A affiliate, the Norfolk Tides. The Mets released Cordero on August 15 after he hit just .129 for the Tides.

After not playing at all in 2006, the Mets signed Cordero to a minor league contract on March 7, 2007, but released him during spring training. Cordero works as a baseball coach during the summers at Kutsher’s Sports Academy in Great Barrington, Massachusetts.