President Carter's multibillion-dollar tax-cut bill to stimulate the economy won final approval from both chambers of Congress yesterday and went to him for his signature.

The bill slashes taxes for individuals and businesses by about $34 billion over the next three years.

Some 46 million taxpayers, 90 per cent of them with incomes under $20,000, will pay an average of $111 less in taxes annually because the standard deduction (for those not itemizing deductions on federal tax returns) will be moved to $2,200 for a single person and $3,200 for a couple filing jointly.

The House cleared the bill 383 to 2 after tacking on a one-year extension of the "countercyclical revenue-sharing" program, which pumps out federal money to the states whenever national unemployment is 6 per cent or higher.

The extension, favored by the White House and approved on a separate 252-to-134 roll call, authorizes $2.25 billion more for the program for the 15-month period ending Sept. 30, 1978. The Senate, which earlier had approved slightly different language, accepted the House countercyclical provision and then the entire compromise tax bill by voive vote.

The bill as a whole means individual and business tax savings of $2.6 billion in fiscal 1977 (which ends Sept. 30), $17.75 billion in fiscal 1979 - a $34 billion total for the three years. The cut was initially higher because Carter, in asking for tax changes to spur the economy in January, included a $50-per-person rebate for individuals on the taxes they had paid on 1976 income. However, when business began doing better than he expected, Carter withdrew his rebate request and it was dropped from the final bill.

Although the change in the standard deduction benefits most taxpayers it affects, for about 2 million single persons with incomes of $13,750 or more, who don't itemize, it means an average tax increase of about $52 per year. Those taxpayers could have gotten deductions of $2,400 under the old law, while now they will be limited to $2,200.

For a married couple with two children, and with an adjusted gross income of $8,000 a year, the standard deduction change will reduce taxes from about $294 a year to $120. The same family with a $15,000 income would be reduced from $1,519 to $1,380 - a $139 saving.

The standard deduction changes, retroactive to Jan. 1, will mean a smaller amount withheld from weekly paychecks of most persons, starting June 1.

The bill also provides for simplified tax forms, so that about 95 per cent of taxpayers will be able to compute taxes from a single table, without having to make separate computations for deductions, exemptions and a special $35 credit.

The bill also extends the $35 tax credit for all taxpayers and their dependents for another year, to the end of 1978, and gives the elderly and blind two such $35 credits per person. The 10 per cent "earned income credit" for those earning under $4,000 also is extended for a year, as are lower corporate tax rates on the first $50,000 of corporate income.

Another major provision grants, for calendar 1977 only, a $28 million tax break for independent oil and gas producers, by absolving them from a 15 per cent "minimum tax" in connection with so-called intangible drilling costs of successful new wells, except to the extent such costs exceed related oil-and-gas income.

One provision in the bill to which the White House voiced strong objections is a special jobs tax credit, designed to induce businesses to hire more workers. It grants a $2,100 tax credit for each employee hired, after allowing for a "normal" 2 per cent growth in the work force. The administration is dubious it will really work.

There is a $100,000 limit a year on total credits for a firm. If the newly hired person is handicapped, the credit is 10 per cent extra.

In all, about $7.4 billion in the bill is for business and the rest for individuals.

Other important provisions:

Postpone for one year, until 1977, new restrictions (passed in 1976) on sick pay deductions (which will mean a $327 million tax saving for persons who received sick pay in 1976), and on taxation of salaries earned abroad (which will mean a $38 million saving for persons employed overseas in 1976).

Allow elderly persons to compute their retirement tax credit for 1976 either on the basis of a new law passed last year or an older one, whichever benefits them more. The elderly will save $30 million in taxes as a result.

Allow tax allowances when a home is used for a day-care business; continue special travel allowances for state legislators; require race-tracks and dog-tracks to withhold 20 per cent of gambling winnings only if the winnings are $1,000 or more and odds are 300-to-1 or more; permit the District of Columbia to garnishee salaries of military and civilian government personnel for child-support; provide a five-year fast-write off on construction of child-care facilities and authorize $870 million over 1978-79 for the work-incentive-program.