Khan was due to fight Lamont Peterson on May 19 in a rematch for the WBA and IBF titles he lost last December via split decision amid controversial circumstances.
However, that fight was called off when it was revealed that Peterson had failed a drugs test which prompted the Khan camp to lobby for him to get his titles back.
Garcia is the WBC champion after defeating Erik Morales for the title in March.
With Ring magazine also offering their title to winner on Saturday it means three world title belts will be up for grabs in Las Vegas.
Peterson still holds the IBF belt.
"Justice has been done," Khan said. "It means this fight (against Garcia) will show who is the best in the division."
"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."