Saudi Arabia is modernizing its eastern fleet, which faces off against Iranian forces across the oil-rich Gulf.
The four ships, based on the US Navy's littoral combat ship, are relatively small but designed to be fast and maneuverable in shallow water and to pack a punch.
The statement from the Defense Security Cooperation Agency said it had notified the US Congress of the State Department's decision and was awaiting final approval.
The agency said the sale would "improve the security of a strategic regional partner, which has been and continues to be an important force for political stability and economic progress in the Middle East."
Dubbed a "multi-mission surface combatant ship" in its export version, the ships carry dozens of Sea Sparrow anti-aircraft missiles and Harpoon anti-ship missiles.
Its main gun is the 76mm OTO Melara, built in Italy, but the main contract for the vessels will go to US arms giant Lockheed Martin.
The sale, if approved as expected, comes amid a renewed arms race in the Middle East.
Russia has stepped up military support for Syria, a bitter foe of Saudi Arabia, and Saudi ally Egypt has agreed to buy two helicopter carrier vessels from France.