Manchin announced Goodwin's appointment during a packed afternoon news conference at the state Capitol.
Manchin said while the Senate seat will always be known as the one Byrd held for more than half a century, "I am truly confident that Carte Goodwin will look out for West Virginians."
Goodwin is expected to be sworn in as a senator Tuesday.
"My responsibility now becomes to work hard every day to maintain the trust of the people of West Virginia," Goodwin said to a crowd thick with media, public officials and well-wishers.
The 36-year-old Charleston lawyer would hold the seat until November. The governor wants general election voters to decide who will serve the final two years of Byrd's term.
Goodwin ruled out running for the seat Friday. Manchin has said it's highly likely that he will seek the seat at election, but has yet to announce his plans.
Byrd was history's longest-serving member of Congress when he died last month at age 92.