White made the announcement on FUEL TV. Shortly thereafter, UFC confirmed the fight on its website.
The bout is scheduled to take place at UFC 156 in Las Vegas.
Aldo (21-1) was scheduled to face Edgar on Oct. 13 at UFC 153 in Rio de Janeiro. But the 145-pound champion was forced to withdraw from the bout after suffering a foot injury.
The injury occurred when an automobile hit the motorcycle Aldo was riding.
Aldo will be making his first appearance inside the Octagon since Jan. 14, when he knocked out Chad Mendes in the first round. That fight took place at UFC 142 in Rio de Janeiro.
The champion was scheduled to fight contender Erik Koch on July 21. That fight was postponed when Aldo suffered a leg injury.
It was rescheduled for Oct. 13, but Koch had to pull out of the bout with an injury -- and Edgar agreed to replace him.
Edgar (14-3-1) lost the lightweight title in February by unanimous decision to Benson Henderson. He also came up short -- via split decision -- to Henderson during their Aug. 11 rematch at UFC 150.
Edgar makes his featherweight debut against Aldo.
Aldo and Edgar are ranked fourth and eighth, respectively, pound-for-pound by ESPN.com.