"The contract was signed and delegations from both sides are negotiating the details," the ministry sources said.
Under the deal, Turkey will get 40 new F-16s and upgrades to 79 of the jets in its existing fleet.
The State Department last week hailed "a major step forward" in Turkey's purchase of new F-16 fighter jets calling them "the most advanced F-16 ever made available only to closest Allies and partners".
"Just the latest example of US enduring commitment to security partnership with Turkey," it said in a social media post.
As required by law, the State Department notified Congress of the agreement in January, as well as a separate $8.6 billion sale of 40 F-35s to Greece.
The United States did not green light the transaction until Turkey's instruments of ratification of Sweden's membership had arrived in Washington.
Turkey's parliament ratified Sweden's NATO membership in January after more than a year of delays that upset Western to unite in the face of Russia's war on Ukraine.
Erdogan is due to join NATO leaders' summit in Washington next month.
He had been set for talks with US counterpart Joe Biden last month but what would have been their first White House meeting was postponed over scheduling problems.
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