WASHINGTON — The House gave final approval on Wednesday to a bill extending health insurance to millions of low-income children, and President Obama signed it this afternoon, in the first of what he hopes will be many steps to guarantee coverage for all Americans.

Smiling broadly, Speaker Nancy Pelosi announced the tally, 290 to 135. Forty Republicans voted for the bill, and 2 Democrats voted against it.

The roll call ended a two-year odyssey for the child health legislation, which President George W. Bush adamantly opposed on the ground it would lead to “government-run health care for every American.”

The Obama White House, battered by a debacle over Tom Daschle’s nomination to be secretary of health and human services, exulted in the passage of the bill, saying it showed how much difference an election could make. Mr. Bush vetoed two similar bills, and the House failed to overturn those vetoes.

Democrats were so sure of victory on Wednesday that the White House scheduled a signing ceremony before the House even passed the bill.

Representative Henry A. Waxman, the California Democrat who is chairman of the Energy and Commerce Committee, said, “While this bill is short of our ultimate goal of health reform, it is a down payment, and is an essential start.”

Ms. Pelosi said that passage of the legislation showed that elections had results.

“This is the beginning of the change that the American people voted for in the last election, and that we will achieve with President Barack Obama,” Ms. Pelosi said.

But Representative Steve King, Republican of Iowa, denounced the bill as “a foundation stone for socialized medicine.”

Another Republican, Representative Tom McClintock of California, said the children’s health program was “slowly replacing employer health plans with government-paid health plans, with spiraling costs to taxpayers.”

Since August 2007, the House has voted at least seven times for legislation to expand the popular State Children’s Health Insurance Program. Prior efforts were thwarted by the Bush White House, which pressed wavering House Republicans to stand firm against the legislation.

The program, created with bipartisan support in 1997, is intended for children in families that earn too much to qualify for Medicaid, but too little to afford private health insurance.

The new bill originated in the House. On Wednesday, the House accepted minor changes made by the Senate, where the bill was approved last week by a vote of 66 to 32, with support from 9 of the 41 Republicans.

The Congressional Budget Office says the bill will enable states to cover more than four million uninsured children by 2013, while continuing coverage for seven million youngsters. The bill will increase tobacco taxes to offset the increase in spending, estimated at more than $32 billion over four and a half years.

In a major change, the bill allows states to cover certain legal immigrants — namely, children under 21 and pregnant women — as well as citizens.

Until now, legal immigrants have generally been barred from Medicaid and the State Children’s Health Insurance Program for five years after they enter the United States. States will now be able to cover those immigrants without the five-year delay.

The bill requires states to verify that people covered by the children’s health program are United States citizens or legal residents. But states are given a new option. Instead of requiring people to produce documents showing citizenship, states can try to verify eligibility by matching a person’s name and Social Security number against federal records.

The bill requires states to cover dental care under the children’s health program, and allows states to provide dental coverage as a supplement to private insurance.

In addition, the bill generally requires states to provide equal coverage of mental and physical illnesses — -- “mental health parity” — -- under the children’s health program.

Democrats like Representative Tammy Baldwin of Wisconsin rejoiced to see the program being expanded.

“Achieving health care for all is the reason I got into politics,” Ms. Baldwin said. “It is my goal, my passion, my motivation. I see real promise that the Obama administration and this Congress will work together to achieve that goal.”

Republicans said the bill did not focus narrowly enough on low-income children. People with private health insurance “will drop it so they can get on the government dole,” said Representative Phil Gingrey, Republican of Georgia.