WASHINGTON—The Pentagon is sending hundreds of troops to Saudi Arabia as part of a buildup to counter potential threats from Iran and its allies, U.S. officials said, marking a U.S. return to the kingdom after its 2003 withdrawal.

U.S. forces will again be stationed at the Prince Sultan Air Base, which had been closed to the American military since the fall of Baghdad following the U.S. invasion of Iraq, officials and experts said.

The...