Judge Monageng and Judge Hofmański found that all criminal acts for which Mr Bemba was convicted fell within the scope of the case that the Prosecutor had brought against him.
But a majority of appeals judges decided Friday that the verdict did not fairly account for Bemba's efforts to stop his troops' crimes once he became aware of them - and that since he was acting as a remote commander, his power to do so was limited.
Bemba's conviction marked several milestones for the ICC.
"This was the first ICC case with a major focus on the use of rape as a weapon of war", she said.
Friday's decision was greeted by cheers from his supporters in the gallery.
Van den Wyngaert said it was up to the trial chamber to decide whether to release Bemba from his 18-year sentence.
The court heard how Bemba sent more than 1,000 fighters to auto back in 2002 to help then President Ange Felix Patasse put down an attempted coup.
In addition, she said trial judges had failed to consider his efforts to stop crimes committed by his Movement for the Liberation of Congo (MLC) once he became aware of them, and how hard it would have been for him to control the troops' actions from a distance. The judges in the minority would have confirmed Mr Bemba's conviction.
Bemba was not released immediately on Friday despite his acquittal because he has also been convicted of witness tampering, and an appeals judgment in that case is still pending.
CAR, meanwhile, has remained in an nearly constant state of turmoil.
A report by Human Rights Watch in October 2017 said fighters in its most recent conflict, which has been raging for more than five years, continued to use sexual violence to "terrorise women and children".
Some of the witnesses who had never been in the military were issued ranks and insignia, according to the summary, and some were promised a new life in Europe.
"I cry with joy because Jean-Pierre Bemba was a dead man".
Their elation was expressed with such vigour the judge called on court staff to restore order.
But the acquittal is a blow for prosecutors. He may not have murdered anyone with his own hands, but as the supreme commander of the Movement for the Liberation of Congo rebel forces, he is responsible for the crimes they committed.