The deal is expected to be completed on Tuesday morning when the teams have a conference call with the league office.
Bynum is expected to be released by 5 p.m. on Tuesday before the second half of his $12.3 million contract becomes guaranteed.
The deal will save the Bulls more than $15 million in salary and luxury taxes, taking them below the salary-cap threshold. In addition, the Cavs will send the Bulls a first-round pick owed to them by the Sacramento Kings that is top-10 protected in the next two drafts.
The Cavs had discussions for more than a week with the Los Angeles Lakers involving a deal for Pau Gasol but could not come to an agreement. The Cavs also had talks about trading Bynum's contract to the Utah Jazz for Richard Jefferson.