During a thirteen-year baseball career, he pitched for the Texas Rangers, Chicago White Sox, San Francisco Giants, Tampa Bay Devil Rays, and Los Angeles Dodgers.

Born in Maracaibo, Venezuela, Alvarez represented his hometown in the 1982 Little League World Series, where they finished with a 2–1 record.

Five days later, he was traded with Scott Fletcher and Sammy Sosa to the Chicago White Sox for Harold Baines and Fred Manrique.

Alvarez provided one of the highlights of the 1991 Chicago White Sox season on August 11, pitching a no-hitter against the Baltimore Orioles at Memorial Stadium in his second Major League start.

Between the majors, minors and winter league play, Alvarez pitched close to 300 innings in 1991; an extremely heavy workload.

During the 1997 season, the White Sox traded Álvarez, Danny Darwin, and Roberto Hernández to the San Francisco Giants for six prospects (Keith Foulke, Bob Howry, Lorenzo Barceló, Mike Caruso, Ken Vining, and Brian Manning) in what became known as the White Flag Trade.