The Bolton boxer lost his WBA and IBF belts in a hotly-disputed points defeat to American Lamont Peterson in Washington last December.
Khan, who was twice docked points for pushing during the contest, raised a number of grievances surrounding the result, including questioning the judging at ringside.
Peterson then tested positive for synthetic testosterone – which he claims is for medical reasons – before their scheduled May rematch.
Golden Boy Promotions chief executive Richard Schaefer has been informed that Khan has been given his title back and will put it on the line in a unification bout with WBC champion Garcia on Saturday.
“Justice has been done,” Khan said before working out in front of the press. “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.”