WASHINGTON—In the three years since a preliminary nuclear deal was struck with Iran, Tehran has received more than $10 billion in sanctions relief from around the world in the form of cash and gold, according to current and former U.S. officials.

The large shipments of gold and cash, from oil funds unfrozen in numerous countries, represent the kind of financial relief that made Iran’s leaders eager to complete the international nuclear accord. Some of the cash and gold went to Iran while the U.S. and other world powers negotiated...