Manchin, a Democrat, named Carte Goodwin, his former chief counsel, last week to serve out the rest of Byrd's term, which ends in January 2013.
Goodwin was sworn in Tuesday by Vice President Joe Biden with Sen. Jay Rockefeller, D-W.Va., at his side, The State Journal in Charleston reported. Goodwin, 36, is the youngest member of the Senate.
But the state Legislature passed a bill Monday requiring a special election this November with a primary Aug. 28, Politico reported. Candidates have until 5 p.m. Friday to file for the race.
Manchin is the only candidate to come forward so far. U.S. Rep. Shelley Moore Capito, a possible Republican candidate, would be able under the special election law to run for the Senate while also running for another term in the House.
Byrd died June 28 at 95. He was first elected in 1958 and at the time of his death was the oldest serving senator and had spent longer in the upper house than anyone else in history.
Manchin paid tribute to Byrd in his announcement, saying, "I would have loved nothing more than for Sen. Byrd were here, to be able to work with him until the end."
Exploding whale video goes viral on Internet
Martin Bashir resigns from MSNBC over Sarah Palin comments