The House yesterday approved a compromise bill to transfer all responsibility for St. Elizabeths Hospital from the federal government to the District by 1991, and sent the measure to the Senate for action.

If the Senate approves the bill, as it is expected to do, it will resolve a longstanding controversy over the future management and funding of the massive, 127-year-old facility. The Reagan administration supports the legislation.

"The plan is to move as quickly as we can with it" on the Senate floor, said Ed Darrell, spokesman for the Labor and Human Resources Committee, which has jurisdiction over the bill. "As far as we know, there are no objections on this side."

The federal government has been trying for years to turn over St. Elizabeths to the District government, which has said it does not want it and cannot afford it.

D.C. Delegate Walter E. Fauntroy said yesterday that the transfer would give the District "greater control over its own mental health system" and predicted that services to D.C. residents would improve as a result. But he voiced concerns about future expenses at the hospital.

"I am disappointed that the [federal] funding was reduced [from an earlier proposed bill], and hope it doesn't work an undue hardship on District taxpayers," he said shortly before the House approval, which came on a voice vote after a brief discussion. "I'm keeping my fingers crossed."

The compromise is the result of intense negotiations by the federal and District governments and the hospital employes' union. St. Elizabeths sits on more than 300 acres in Southeast Washington and has about 1,800 inpatients.

Under the measure, property and management of St. Elizabeths will be transferred to the District in October 1987. The federal government will provide a total of $219 million between fiscal 1986 and 1991, and then will be released of all future financial responsibility.

The bill requires the city to develop and implement a community-based mental health system by 1991, a move which ties in with a court-ordered deinstitutionalization of mental patients to the least restrictive setting possible.

Current federal hospital employes would receive job protections, including priority in hiring in the new D.C. mental health system and guarantees they will not lose pay, seniority or benefits.

The compromise represents some last-minute concessions on the part of the city government over how much money the federal government will provide in transition costs. These were necessary to resurrect the measure in the closing days of the 98th Congress after the Reagan administration torpedoed an earlier version with objections that surprised House members as they were about to bring the legislation to the floor two weeks ago.

Total federal funding was reduced from $307 million in the scuttled version of the plan, to the $219 million approved yesterday.

"We are pleased that we could work out an agreement with the administration and that the House passed it before they adjourned," said Annette Samuels, spokeswoman for Mayor Marion Barry. On the question of the money in the bill, "We accept that," she said.

Left unanswered is what will happen to the St. Elizabeths property that the city does not need for its new mental health system.

The District last week had succeeded in getting a provision added to the proposed compromise to remove the historical landmark designation from the hospital to give the city more flexibility for future development of the property.

However, this amendment ran into difficulties with historical preservationists, congressional aides said, and the bill's sponsors decided not to remove the designation.

St. Elizabeths has faced impending financial crises for a number of years as the federal and city governments have sparred over what share each is responsible for paying.

A final resolution on its future would free up $20 million in federal funds put in the District's fiscal 1985 appropriations bill -- still awaiting final congressional approval -- contingent upon adoption of such a plan.

House District Committee Chairman Ronald V. Dellums (D-Calif.) called the compromise "a well worked out balance of federal and local interests." Rep. Stewart B. McKinney (R-Conn.), ranking Republican on the committee, said it was "something we should have taken care of years ago."

And Rep. Stan Parris (R-Va.), a committee member, said the bill gets the federal government out of St. Elizabeths at a reasonable cost and turns the mental health system over to the city, "where it belongs."