Prior to his MLB career, Speier attended the University of San Francisco and was also a U.S. Marine Corps reservist. He was drafted by the Chicago Cubs on June 1, 1995 and immediately placed with the Cubs minor league affiliates.

On May 27, 1998, Speier made his MLB debut with the Cubs, playing just a single game with the Cubs before being traded to the Florida Marlins on July 31, 1998. He finished the 1998 season with the Marlins, playing in 18 games, pitching 19.3 innings.

Just before the start of the 1999 season, Speier was traded to the Atlanta Braves, on April 1, where he split the season between the Braves and their minor league team. Speier was waived following the 1999 season, then claimed on November 23, 1999 by the Cleveland Indians.

He continued with the Indians for the next season and a half, when on May 19, 2001 he was traded to the New York Mets, then waived. Just 10 days later, Speier was claimed by the Colorado Rockies, where he finished the 2001 season and stayed for an additional two years.

On December 14, 2003, Speier was was part of a three team trade that sent him to the Toronto Blue Jays. He averaged roughly 60 games a year with the Blue Jays over the next three seasons, his most successful season coming in 2005 where he finished with a 2.57 ERA. Speier was waived following the 2006 season.

On November 19, 2006, Speier signed as a free agent with the Los Angeles Angels of Anaheim. He made his first post season appearance with the Angels in 2007, where they lost the American League Divisional Series to the eventual World Series Champions, the Boston Red Sox.