Kolb was drafted by the Texas Rangers in 1995 and made his major league debut with Texas in 1999. He spent that season and the next three being shuttled between the Rangers and their minor league system. Released before the 2003 season, he signed as a free agent with the Milwaukee Brewers, where he became the team closer and shined in that role during the 2003 and 2004 seasons, converting 60 of 67 save opportunities, and was selected to the NL All-Star team in 2004.

Before the 2005 season, the Atlanta Braves returned closer John Smoltz to his original starter role to compensate for several losses in their pitching rotation. The Braves traded highly regarded rookie pitcher José Capellán and minor league pitcher Alec Zumwalt to the Brewers for Kolb to replace Smoltz in the bullpen. However, Kolb endured a poor season with the Braves, going 3-8 with a 5.93 ERA while recording only 11 saves before being replaced in the closer role by Chris Reitsma. Because of his struggles, Kolb was consistently booed at Braves' home games and had derogatory websites devoted to him and also, per noted Braves' historian Barry Garrett, became the most hated Braves' pitcher of all time. He admitted following the '05 season that the pressure of replacing a legend like Smoltz played a big part in his ineffectiveness.

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