Puzder, a food-chain owner, withdrew his nomination facing opposition from some Republican senators, which seemed to have made his confirmation hard.
Puzder was set to appear Thursday before the Senate Health, Education, Labor and Pensions Committee for his long-delayed confirmation hearing to lead the Labor Department.
U.S. Sen. Elizabeth Warren, D-Massachusetts, who sent a 28-page letter to Puzder Monday seeking answers about labor discrimination lawsuits against his company, called for him to withdraw from the nomination during a Wednesday floor speech.
"He's intense, hardworking, but I think in contrast to Puzder, he's going to get things done more quietly", said Tammy McCutcheon, who served as administrator of the Wage and Hour Division of the Labor Department during the Bush administration.
Acosta, a native of Miami who graduated from Harvard Law School, became dean of the FIU law school in 2009, according to his bio on the college's website.
The announcement was expected at a hastily-arranged press conference at the White House.
President Donald Trump is considering at least four candidates to be his new nominee for labor secretary after his previous pick abruptly withdrew from the confirmation process. In addition, Puzder disclosed last week that he failed to pay taxes for an undocumented housekeeper. Only one other pick - Rex Tillerson to serve as secretary of state - drew as much public wavering among Republicans ahead of his hearing, when five GOP senators expressed doubts.
Senate Democratic Leader Chuck Schumer fanned the flames behind the opposition to Puzder in a statement Wednesday afternoon.
Additionally, Puzder's ex-wife accused him of physical abuse in a 1990 episode of "The Oprah Winfrey Show", although she has since retracted the allegations.