Acosta is a former federal prosecutor in Florida and now the dean of the law school at Florida International University (FIU). He has also served on the National Labor Relations Board and led the Justice Department's civil rights division.
Acosta was tapped one day after Trump's first nominee for the post, Andrew Puzder, withdrew under pressure over his business record and other past controversies in his personal life.
"I think he'll be a tremendous secretary of labor," Trump said of Acosta at a White House news conference. "He has had a tremendous career."
Acosta served as federal prosecutor in Florida for nearly a decade, departing in 2009 after prosecuting high-profile cases involving former lobbyist Jack Abramoff, the Liberian torturer known as Chuckie Taylor and Colombian drug cartel members.
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Trump had faced criticism for not nominating any member of the Latino or Hispanic community to his inner circle, despite the nation's Hispanic population topping 17 per cent.
Cabinet members require confirmation by the US Senate. Puzder, a fast-food executive who faced intense criticism for his labor policies including opposition to minimum-wage increases, withdrew after it became clear he did not have sufficient votes.
He has already been confirmed three times by the Senate for various posts, suggesting he should have a smoother ride than the previous nominee.
In March 2011, as the tenth anniversary of the 9/11 attacks neared, Acosta testified before a Senate judiciary panel about protecting the civil rights of American Muslims.
"These efforts following 9/11 were important. They set a tone," he told Congress. "They reminded those who might be tempted to take out their anger on an entire community that such actions were wrong.