The Briton lost his WBA and IBF belts in a hotly-disputed loss to Peterson in the Washington fighter's hometown last December.
Khan raised a number of grievances surrounding the result and was further vindicated when Peterson tested positive for synthetic testosterone before their scheduled May rematch.
Golden Boy Promotions chief executive Richard Schaefer said that the WBA informed him that Khan has been given his title back and will put it on the line in a unification bout with WBC champion Danny Garcia on Saturday.
"Justice has been done," Khan said. "I'm glad the WBA are reinstating me as champion, it means I walk into this fight as world champion.
"There is a chance to win the WBC belt as well but not only that, the Ring magazine title will be on the line as well.
"It means this fight will really show who is the best fighter in the 140lb division."
Meanwhile, David Haye is unrepentant that Saturday's domestic showdown with Dereck Chisora is going ahead.
Upton Park will stage the eagerly-awaited grudge match which will see the British rivals settle their differences after brawling at a press conference in Munich five months ago.
Objections have been raised to them profiting from the out-rageous scenes with almost universal condemnation greeting their behaviour that night.
Haye, however, has a simple message for those opposed to the staging of Saturday's bout.
"If you're so disappointed, stop looking at it on YouTube," he said.
"It's had 20 million hits. People are looking at it. If I'm disappointed in something, I'm not going to keep looking at it."