The 25-year-old lost the strap to the American, along with his IBF title, in December's controversial points defeat in Washington.
However, the 2004 Olympic silver medallist will now walk to the ring at the Mandalay Bay in Las Vegas as WBA champion.
"I'm delighted. This is great news and a real boost for me coming into the return," said Khan.
Peterson remains the IBF champion, meaning the eagerly-anticipated clash is now billed as a unification bout.