The Queen City was rocked by riots in April after a white police officer shot and killed an unarmed black youth.
More than 3,000 tickets had been sold for Cosby's March 15 appearances.
"I still stand by the fact that I feel very uncomfortable playing the concerts at this time in this climate," Cosby said in a statement issued Wednesday.
The Coalition for a Just Cincinnati praised Cosby's decision
"We're very happy and elated over the situation and the fact that a man of Bill Cosby's stature and valued personality would back the cause that we are fighting for here in Cincinnati," the Rev. J.W. Jones, a spokesman for the group, said.
The Cincinnati Black United Front has contacted the Progressive National Baptists, urging that group to cancel is scheduled August convention in Cincinnati. The Baptist group had planned to bring 8,000 delegates to the city and convention organizers said they planned to discuss the situation later this week.
Mayor Charlie Luken said he tried to contact Cosby but was told the entertainer thought the timing of his appearance was "inappropriate."
Luken called the boycott ill-advised.
"I think people who are encouraging the boycott are actually hurting themselves because that means some waiter won't get their paycheck that night," Luken told the Cincinnati Post.
The coalition, however, believes the city has not done enough to address racism.
All it would take is for people of power to set a table to discuss our grievances," Jones said.