Bradley controversially beat Pacquiao when they first met in 2012 but the Filipino gained revenge in their 2014 re-match, scoring a unanimous decision win to regain the WBO welterweight title.
Next April's bout will be Pacquiao's first since he lost a unanimous decision to unbeaten American Floyd Mayweather Jr. in the so-called "Fight of the Century" in Las Vegas seven months ago.
Pacquiao, the former eight-division world champion, was hampered by a torn rotator cuff against Mayweather before undergoing arthroscopic surgery on his right shoulder just four days later.
Pacquiao had been expected to retire, with little left to prove after achieving his long-stated goal of getting in the ring with Mayweather, but then said in October that he would return for one more fight in 2016.
According to Pacquiao's promoter Bob Arum, the Filipino could well have additional bouts in his sights before he finally decides to call time on his career.
"I don't want to say that (it's his last fight)," Arum told Reuters via telephone.
"I'm not going to sell it as that because I don't want everybody to say, 'Hey, it's his last fight, come and see it!' and then it turns out that it's not his last fight.
"Who the hell knows with these guys? They all change their minds so I'm not selling it as his last fight. He says it's his last fight but who the hell knows?"
Southpaw Pacquiao, who has a 57-6-2 record with 38 knockouts, will be taking on a two-time WBO welterweight champion in Bradley (33-1-1, 13 KOs).
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Andrew Both)
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