WASHINGTON — President Bush yesterday signed legislation designed to make college more affordable for students from poor and middle-class families, swallowing objections to a bill that enjoyed veto-proof majorities in Congress.

The new law achieves a goal Mr. Bush shares with lawmakers: boosting aid for needy students. The action allows both the Bush administration and Congress to say they have done something to ease the burden of paying for college, a popular political priority. “I have the honor of signing a bill that will help millions of low-income Americans earn a college degree,” Mr. Bush said in a ceremony, with lawmakers and students by his side. The legislation boosts the maximum Pell grant, which goes to the poorest college students, from $4,310 a year to $5,400 a year by 2012.

It also cuts in half the interest rates on federally backed student loans — from 6.8% to 3.4% — over the next four years.

The increase in financial aid is designed to come from cuts in subsidies that the government makes to banks, totaling roughly $20 billion. Boosting college aid was one of a half-dozen domestic priorities Democrats set when they took control of Congress this year.

Mr. Bush at one point threatened to veto the bill on grounds that it included hidden costs and was an expensive expansion of federal programs. Yet he went along, despite what his administration still calls budget “gimmicks” in the legislation, mainly because of the increased aid for poor students, one of his longtime priorities.

“Pell grants send an important message to students in need,” Mr. Bush said. “If you work hard, and you stay in school, and you make the right choices, the federal government is going to stand with you.”

Congress overwhelmingly backed a compromise version of the student-aid bill earlier this month. The House approved it 292–97; the Senate vote was 79–12. All the lawmakers who voted against the bill were Republicans.