The first song eligible to be claimed back is "Love Me Do," in October 2018. The rest of the catalog would follow in years after, ending in 2026.
McCartney wants a ruling to say his claiming them doesn't represent a legal breach of any contract or publishing agreement that Sony/ATV could use against him.
"Defendants have attempted to reserve their rights to challenge Paul McCartney's exercise of his termination rights on contractual ground," the filing says.
It adds, "A judicial declaration is necessary and appropriate at this time so that Paul McCartney can rely on quiet, unclouded title to his rights."
Sony/ATV said it had "the highest respect" for McCartney.
"We have collaborated closely with both Sir Paul and the late John Lennon's Estate for decades to protect, preserve and promote the catalog's long-term value," the company said, adding that it was "disappointed" over the filing of the lawsuit, which it said is "unnecessary and premature."
The lawsuit also said Sony/ATV attempted to stall talks with McCartney until the conclusion of a separate lawsuit involving similar claims by British pop band Duran Duran in an English court. Duran Duran lost the legal battle to a Sony/ATV subsidiary in December.