If confirmed, Acosta will be the first Latino appointed to Trump's cabinet.
Acosta has been the dean of the law school at Florida International University since 2009.
He previously served as assistant attorney general for the Justice Department's Civil Rights Division under President George W. Bush, a post he was given in August 2003.
In addition to being a member of the National Labor Relations Board, the labor secretary-designee was a U.S. attorney for the Southern District of Florida.
“Throughout his career, Alex Acosta has been a passionate advocate for equal opportunity for all Americans,” Trump said. “His extensive experience has tremendously impressed me and my team and makes us confident that he will lead the Department of Labor with the utmost competence and determination to support the American worker.
Trump announced his pick just one day after his last nominee for the post, Andrew Puzder, withdrew his name from consideration. Puzder had been dogged by criticism amid disclosures that he had hired an undocumented worker as a housekeeper and that he'd been accused of domestic abuse by his ex-wife.
Acosta is a native of Miami, Florida. He went to Harvard Law School and also got his bachelor's degree in economics from Harvard.
Before Samuel Alito became a Supreme Court justice, Acosta clerked for the judge on the U.S. Court of Appeals for the Third Circuit.
Acosta later worked for the Washington law firm of Kirkland & Ellis, specializing in employment and labor issues. During this time he also taught classes on civil rights, employment and disability law at the George Mason University School of Law.
During his years as U.S. attorney for the Southern District of Florida, Acosta prosecuted a number of high-profile defendants, including Jack Abramoff for fraud and Jose Padilla for terrorism.
On his watch, the district also prosecuted several bank-related cases, including one against Swiss bank UBS.
UBS eventually paid $780 million in fines. The case is also noteworthy because UBS provided the government with the names of individuals who were using secret Swiss bank accounts to avoid U.S. taxes.
Trump spent spent relatively little time talking about Acosta during his announcement, spending most of his time at the podium attacking the media, which he said is only interested "in serving the special interests."
"This is a tremendous disservice to the American people," Trump said. "The press is out of control and the level of dishonesty is out of control."
Trump touted a presidential-tracking poll released Wednesday by Rasmussen Reports that found 53 percent of likely voters approve of his performance in the White House, while 47 percent disapprove.
The poll found also that 37 percent “strongly approve” of Trump's actions since his inauguration and 38 percent “strongly disapprove.”
"I ran to serve the people and fix a broken system so that it serves the people well ... and I'm doing what I promised on the campaign trail," he said. "The media won't tell you that; I don't know why.
"This administration is running like a finely tuned machine - despite the fact I can't get my cabinet approved," Trump said.
"This past month has been unprecedented in history," Trump added. "There has never been a presidency that's done so much in so short a time. And we're just getting started."
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