Congress made history yesterday as it game final approval to $35 billion in spending cuts for next year that dramatically reverse nearly half a century of ever-expanding government involvement in the nation's social welfare.

Voting by voice, the Democratic-controlled House overwhelmingly approved a conferees' compromise that gives President Reagan almost all of the budget reductions that he sought less than five months ago: a total of more than $130 billion over the next three years.

Within a couple of hours, the Republican Senate followed suit, voting 80 to 14 to send the unprecedented measure to Reagan for his signature.

Although the Democrats claimed to have samed about $3.5 billion worth of programs in House-Senate negotiations over the final product, it was a major triumph for Reagan and his brand of fiscal conservatism that resulted in slashing up to 250 domestic spending programs, the once-cherished legacies of the New Deal, Fair Deal, New Frontier and Great Society.

Deep cuts were approved in education, health, welfare, employment, nutrition, retirement and other programs. Some programs, such as public service jobs, will vanish. Democrats succeeded in preserving the structuire of some threatened programs and prevented many others; from being submerged into block grants to the states. But, even on block grants, where Reagan succeeded least, he won partial victories.

The Democrats ended the day with only one political trophy: a 404-to-20 House vote for legislation to restore the $122-a-month minimum Social Security benefit that is being eliminated in the huge budget "reconciliation" bill.

But even that victory was marred by the fact that the Senate Republican leadership, over futile protests from defeat-scarred Democrats, succeeded in shelving consideration of the proposal until after Congress returns from its five-week summer recess that starts next week. Nonetheless, Democrats can now blame the Republicans for thwarting restoration of the benefit.

The spending cuts were the biggest ever voted by Congress, passed with extraordinary speed under relentless pressure from Reagan and his hard-driving budget director, David A. Stockman.

Even the Democratic-controlled House buckled repeatedly, twice opting for Reagan's spending blueprint over a Democratic alternative and buying his tax cut plan as well. Together, the tax and spending cuts will give the president the twin pillars of his economic program within his first 200 days in office.

Republicans hailed the legislation as a harbinger of economic recovery, but Sen. Edward M. Kennedy (D-Mass.) decried it as "the product of an economic theory that says we can have prosperity only by abandoning the social progress of a generation."

The program cuts, affecting neraly every aspect of government except defense, are aimed at keeping the government within its budget of $695.3 billion and projected deficit of $37.6 billion for the 1982 fiscal year starting Oct. 1. The administration says they are a first step toward a balanced budget by 1984, but that will require still more cuts later.

Largely because of huge increases in defense spending, actual outlays will continue to grow next year, but not as fast as before. The budget ceiling of $566.4 billion for 1980 rose to $661.4 billion by the end of fiscal 1981, an increase of nearly $100 billion. By way of contrast, the spending target for 1982 is only $34 billion over the 1981 ceiling.

"No other exercise in fiscal restraint comes close" to Reagan's program, said Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) as the House-Senate budget conference -- itself a record-making assemblage of more than 250 conferees meeting in 58 separate mini-conferences -- wrapped up its work last Wednesday. "A crucial step in restoring national economic sanity," Sen. William L. Armstrong (R-Colo.) called it in yesterday's debate.

But House Budget Chairman James R. Jones (D-Okla.) described it differently. "We're not just cutting fat," said Jones, asserting that the cuts will have a "direct and damaging impact on the lives of millions of Americans."

Jones accused the Republicans of overloading the budget-cutting process and asserted: "We've seen reconciliation used as it was never intended, and I hope this will never happen again."

But even Democrats acknowledged that the bill made history. "What is before the House is historic," said Rep. Leon E. Panetta (D-Calif.), one of the Democrats' budget experts. "It is historic in terms of its impact on people and their relationship to government. It is historic in terms of its impact on the budget process."

On the Social Security issue, the Democrats were laying the groundwork for what they see as an inevitable backlash against Reagan's more drastic cuts. But Congressional Republicans, sensing trouble over Social Security cuts, have promised to consider some ameliorating action this fall. And White House spokesman David Gergen said yesterday that the administration will explore relief for at least 300,000 of the three million minimum-benefit recipients, those whom he described as "truly needy."

The benefit will not be eliminated before December for future retirees and March for those now on the rolls, giving time for second-thoughts. But this, complained House Majority Leader James C. Wright Jr. (D-Tex.), is "like being on a jury and voting to hang an innocent man in February upon the premise that the goernor's going to reprieve him in the meantime."