UFC president Dana White confirmed the news, first reported by USA Today, to ESPN.com's Franklin McNeil.
Edgar (14-3-1) replaces injured 23-year-old Erik Koch (13-1). White told USA Today on Thursday that he learned Koch could not fight.
One call from White to Edgar and UFC locked down a long-talked about contest between two of ESPN.com's top 10 pound-for-pound fighters in mixed martial arts.
"The fans want this fight. I want this fight. The UFC wants this fight. Let's do it," Edgar told his manager.
Edgar held the UFC lightweight title from April 2010 until February of this year, when he lost a close decision to Benson Henderson. After a second tight decision loss to Henderson on Aug. 11, Edgar announced he would drop 10 pounds to campaign at featherweight.
Abdel-Aziz said Edgar has returned to the gym and was training in preparation for the move.
"He doesn't have much weight to cut," Abdel-Aziz said. "He walks around at 158, 157. He's not going to cut much at all."
Edgar earned a reputation for fighting bigger opponents, and even though he's coming down in weight, he may face that scenario against Aldo (21-1). The young Brazilian champion has been a force in the division, winning each of his 11 bouts under the Zuffa banner at 145 pounds. After beating Manny Gamburyan in September 2010 to defend the World Extreme Cagefighting belt, Zuffa promoted Aldo to UFC champion. He has defended that title three times, the latest a first-round stoppage of Chad Mendes this January at the HSBC Arena in Rio, which will host his contest against Edgar.
Information from ESPN.com's Franklin McNeil was used in this report.