An Alexandria company that plans to make compost out of the District of Columbia's sewage sludge and trash finally succeeded yesterday in buying a 195-acre estate in King George County, Va. as the location for the controversial facility.

Sale of the Chatterton Estate on the Potomac River had been held up for two weeks after a storm of opposition to the project developed among residents in King George.

"The settlement went through today," said Robert N. Picardat, vice president of Dano Resource Recovery Inc., the company that has $32.5 million in contracts with the District. "We bought the estate for $495,000 in cash."

The seller was Washington attorney Donald S. Dawson, whose decision to sell aroused opposition from some of his neighbors in the Northern Neck county 50 miles south of Washington.

Dano plans to begin construction of the composting facility on Monday, despite the county's decision last month to revoke the compay's building permit. The county took the action because the Board of Supervisors concluded that Dano's construction plans were inconsistent.

The supervisors, like protesting citizens who had organized the King George County Environmental Association after Dano's plans became known last fall, did not want the county to become a disposal center for the District's sewage sludge and trash.

Under contracts between the city and Dano, 800 tons of sludge and 900 tons of trash would be shipped each day by barge to the facility in King George.

The District is under court order to find a place to dispose of its ever-mounting share of sludge from the regional sewage treatment plant at Blue Plains. Originally the city wanted to build a composting facility at Oxon Cove near Blue Plains at the southern tip of the city, but nearby residents opposed the project, which was then dropped by the administration of former Mayor Walter E. Washington.