Acosta became the latest of several Trump cabinet members to leave in the midst of scandal or disagreement with the president.
"I am pleased to announce that it is my intention to nominate Gene Scalia as the new Secretary of Labor," Trump tweeted.
"Gene has led a life of great success in the legal and labor field and is highly respected not only as a lawyer, but as a lawyer with great experience working with labor and everyone else."
Eugene Scalia is currently a partner with Gibson, Dunn and Crutcher's Washington office.
The firm's website says he handles "a broad range of labor, employment, appellate, and regulatory matters" and he previously served as the Department of Labor's top legal officer.
Acosta was the only Hispanic member of Trump's cabinet, which is pushing deregulation across a number of sectors including labor. But business leaders felt Acosta didn't move fast enough on rolling back labor rules, The Washington Post has reported.
A former federal prosecutor, Acosta had faced mounting calls to quit over a secret plea deal he negotiated a decade ago with Jeffrey Epstein, a financier accused of sexually abusing underage teen girls.
The White House began considering Scalia for the position as the scrutiny over Acosta's plea deal began to intensify last week, the Post reported, adding that Trump and Scalia met privately Thursday afternoon at the White House to discuss the job.
Eugene Scalia's late father, conservative justice Antonin Scalia, served on the US Supreme Court for 30 years, from 1986 until his death in 2016.