Bogans had an option for $1.73 million, and he became expendable when the Bulls signed free agent Richard Hamilton on Wednesday.
"We have a great appreciation for what he did," Bulls coach Tom Thibodeau said Friday. "I thought he had an unbelieveable year for us last year. He filled his role great, played great defense each and every night. Knocked down open threes. He's the consummate professional and we wish him well."
A favorite of Thibodeau's because of his defense, Bogans started all 82 games and averaged 4.4 points in 17.8 minutes a game last season.
The Bulls also waived guard Jannero Pargo, who spent 14 games on the team's inactive list last season.
ESPNChicago.com's Nick Friedell contributed to this report.