Business leaders are predicting a dramatic unraveling of regulations on everything from overtime pay to power-plant emission rules as Donald Trump seeks to fill his cabinet with determined adversaries of the agencies they will lead.

The president-elect’s pick Thursday to head the Labor Department, fast-food executive Andrew Puzder, is an outspoken critic of the worker-pay policies advanced by the Obama administration. Mr. Trump’s choice for the next administrator of the Environmental Protection Agency, Oklahoma Attorney General...