After prolonged negotiations, the District government has signed a lease granting docking rights to a private corporation that plans to open a 200-seat restaurant on a boat on the Georgetown waterfront by 1987.

The boat will be docked along the Potomac River between 33rd Street NW and Key Bridge.

The 35-year lease, which was signed Sept. 6 and effective when the restaurant opens, calls for a smaller floating restaurant than originally proposed and represents a compromise between the developer, the U.S. Park Service and Georgetown residents.

The developer, Williamsburg Inc., initially proposed to turn the USS Williamsburg, a former presidential yacht, into a 500-seat dining facility and to lease 2.6 acres of waterfront property for parking.

But opposition from Georgetown residents led to an agreement to custom-build a smaller boat, leaving the fate of the Williamsburg uncertain. The company is getting parking space for 86 cars and will use the city's old motor vehicle impoundment lot temporarily, but eventually will move to another site away from the waterfront.

The developers have agreed to pay the District a minimum yearly rent of $18,000 or 1 1/2 percent of annual gross sales, whichever is greater. But the rent would be reduced, at least in the initial years of the restaurant's operation, because the lease calls for giving rental credits to the firm for Park Service-ordered landscaping improvements and sea wall repairs.

The Williamsburg, now anchored near the Blue Plains sewage treatment plant in Southwest Washington, must be moved from there by the end of the year.