MILAN—Fiat Chrysler Automobiles NV and Peugeot maker PSA Group of France agreed to a nearly $50 billion merger that, if concluded, will mark one of the biggest auto industry consolidation deals in two decades.

Fiat Chrysler and PSA shareholders will each initially own 50% of the new entity, both companies said Thursday in a joint statement, confirming reporting from The Wall Street Journal.

John...