The two carriers are dropping an appeal of the initial decision to clear the way for a new case.
When the DOT denied approval last year, it said the carriers' proposal "would be insufficient to preserve competition at the two airports."
Delta and US Airways contend that since their original proposal in 2009, low-cost carriers including AirTran Airways, JetBlue Airways and Southwest Airlines have "gained considerable access to slots" at LaGuardia and Reagan. They also say the United-Continental and Southwest-AirTran mergers have "dramatically sharpened competition on the East Coast generally and particularly in the New York and Washington regions."
The DOT previously said it would only approve a deal if the carriers sold 14 slot pairs -- one takeoff and one landing -- at Reagan and 20 at LaGuardia to other airlines through a blind auction.
In the new proposal this week, the airlines said that if required, they would divest up to eight at Reagan and 16 at LaGuardia in a DOT-approved process.
With the slot swap, Delta would get 132 slot pairs at LaGuardia from US Airways, and US Airways would get 42 at Reagan from Delta. That would give Delta seven more slots in New York than in earlier versions of the deal.
Along with the slot swap, Delta will pay US Airways $66.5 million in cash in the new version of the deal.