As required by US law, the State Department notified Congress of the agreement, as well as a separate $8.6 billion sale of 40 F-35s to Greece.
Turkey will get 40 new F-16s and upgrades to 79 of the jets in its existing fleet, the State Department said in a news release, reports AFP.
The United States did not green light the transaction until Turkey's instruments of ratification of Sweden's membership had arrived in Washington, a US official said, highlighting the highly sensitive nature of the negotiations.
All instruments of ratification must be deposited in the US capital -- a city NATO Secretary General Jens Stoltenberg will visit next week, and which will host a summit in July to mark the 75th anniversary of the trans-Atlantic alliance.
Turkey's parliament ratified Sweden's NATO membership on Tuesday after more than a year of delays that upset Western efforts to show resolve in the face of Russia's war on Ukraine.
Turkish President Recep Tayyip Erdogan initially objected to Sweden's NATO bid over Stockholm's perceived acceptance of Kurdish groups that Ankara views as "terrorist" organizations.
Sweden responded by tightening its anti-terrorism legislation and taking other security steps demanded by Erdogan.
But Erdogan then turned to an unmet US pledge to deliver a batch of F-16 fighter jets that has met resistance in Congress because of Turkey's perceived backsliding on human rights and standoffs with fellow NATO member Greece.
The powerful chairman of the Senate Foreign Relations Committee, Democrat Ben Cardin, said Friday he would permit the F-16 sale to Turkey but that it was "not a decision I came to lightly."
US Secretary of State Antony Blinken led an intense diplomatic effort to broker the deal, telling the Turkish president three times during a trip to Ankara just after the February 2023 earthquake that there would be no planes if Turkey blocked Sweden's NATO bid, the US official said.
Athens meanwhile strongly opposed the sale due to unresolved territorial disputes with Turkey in the energy-rich Mediterranean region.
The US agreement with Turkey hinged first on Athens not obstructing the sale, and Greece was simultaneously granted more advanced F-35s.
Bd-pratidin English/Lutful Hoque