Born in Maracaibo, Venezuela, Alvarez represented his hometown in the 1982 Little League World Series, where they finished with a 2-1 record. Alvarez began his professional baseball career when he was signed by the Texas Rangers as an amateur free agent on September 23, 1986. He made his major league debut at the age of nineteen on July 24, 1989. 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 only his second Major League start. It was quite a contrast to his only previous appearance, when he faced five batters for the Rangers and gave up two walks, a single and two home runs without retiring a batter, giving him a career ERA, prior to his no-hit gem, of infinity. Alvarez had control problems in the minors, and it carried over to the big leagues. After shouldering a very heavy workload in 1991, he was kept under scrutiny for most of the season. Between the majors, minors and winter league action, Alvarez worked close to 300 innings in '91; a significant number for anyone, but especially for a 21-year-old pitcher. It wasn't until that he managed to break into the rotation permanently. That season, Alvarez won 15 games and finished second in the league in earned run average, but his control problems continued; he led the league with 122 walks. In, Alvarez went 12–8 and made the American League All-Star team. After a disappointing 8–11 in, he had 15 wins and 181 strikeouts in. During the season, the White Sox traded Álvarez, Danny Darwin, and Roberto Hernández to the San Francisco Giants for six prospects in what became known as the White Flag Trade. A free agent after the season, he signed a five-year contract with Tampa Bay. He was the team's first pitcher, and started Opening Day on March 31, 1998, throwing the Devil Rays' first ever pitch. Inconsistency and poor conditioning continually kept him from realizing his full potential. In his first season with the Devil Rays, Alvarez missed two months with tendinitis in his shoulder, eventually losing 14 games during the season. The following year he made two trips to the disabled list. Finally, he had arthroscopic shoulder surgery and missed the next two seasons. After finishing his contract with Tampa Bay, Álvarez signed with the Dodgers. He began the 2003 season as a starter for Triple-ALas Vegas. After going 5–1 with a 1.15 ERA, he filled the long relief role for the Dodgers at mid-season. Later he got a chance to start, collecting a 5–0 record and 1.06 ERA over a stretch of nine games. In 2004, he went 7–6 in 40 games. On August 1, 2005, Alvarez announced he would retire after the season. He compiled a career 102–92 record with 1330 strikeouts and a 3.96 ERA in 1747.2 innings. After a brief stint as the pitching coach of the State College Spikes, Álvarez joined the Baltimore Orioles organization when he was named pitching coach of the Gulf Coast League Orioles in 2013. He was dismissed from that job in June 2019. In 2010, Álvarez gained induction into the Caribbean Baseball Hall of Fame.
Personal life
He is the father of Viviana, Vannessa, and Valentina Alvarez, and currently lives in Florida.