In , Keith found a home in the White Sox bullpen, primarily serving as set-up man for closers Matt Karchner (who was traded to the Chicago Cubs in the middle of the season) and Bill Simas. In , Foulke established himself as one of the league's best relief pitchers, posting a 2.22 ERA in 105.1 innings of work over 67 games, however, he was still used primarily as a set-up man. His stellar season even netted him a vote for the 1999 AL Cy Young Award.
In , Foulke again was an important piece of the White Sox bullpen, however, Bob Howry entered the season as the team's primary closer, though Foulke was seeing more and more time closing out games, and by April's end he had recorded 4 saves (in 1999, he didn't notch a save until June). As Howry continued to struggle, Foulke inherited the closer's role and flourished, saving 34 games for the White Sox in 2000, and was a major reason the White Sox won the AL Central title.
On December 3, , Foulke, along with catcher Mark Johnson, minor league pitcher Joe Valentine, and cash, was traded by the White Sox to the Oakland Athletics for closer Billy Koch and two minor leaguers. During the season with the Athletics, Foulke would distinguish himself as a closer, leading the league in saves and games finished, being named to the All-Star team and winning the American League Rolaids Relief Man of the Year Award. However, it was Foulke who also gave up the game-winning double to David Ortiz in Game 4 of the American League Division Series that year.
"They're not going to make it any harder than it is for me to go home and look in the mirror," Foulke said about the booing that rained down from the stands on a sticky night in the Fens. "Like I've told you guys plenty of times, I'm more embarrassed to walk into this locker room and look at the faces of my teammates than I am to walk out and see Johnny from Burger King booing me. I'm worried about these guys, not everybody else.
Foulke's perceived lack of respect for Red Sox fans made him a target for both fans and the Boston media alike. His baseball heart was also questioned because he said he did not care if he was a closer, but clarified, "I love to pitch. I don't care if I pitch in the second inning, the fourth inning, the ninth inning, the 10th inning. I didn't ask to be a closer. It's just the job that I do." The media also had a field day when they found out that Foulke demanded a new truck as compensation for his weekly interviews with Dale & Holley on WEEI.
Foulke has good control, as his career strikeout-to-walk ratio reveals. While he doesn't hold runners on base particularly well, he covers his position adequately and throws accurately to the bases. In 2004, he completed a fifth straight season without committing an error (71 total chances in 307 games). In addition, his relatively unique throwing motion provides him with the ability to mask his changeup well, though runners on base can easily see his grip from his exposed hand and potentially tip his pitches to teammates at-bat.