* Senate committee drafting student loan bill-aide

* FFELP program would be killed under House bill

* Obama praises House bill in university speech (Adds White House comments)

WASHINGTON, Sept 17 (Reuters) - The biggest change in U.S. higher education finance in 35 years was approved on Thursday by the House of Representatives, handing a defeat to major banks and student loan giant Sallie Mae SLM.N.

Lawmakers voted 253-171 in favor of legislation that would cut the banks and Sallie Mae out of a large slice of the $92 billion college student loan business, shifting most lending into a program run by the U.S. Education Department.

The bill, supported by the White House, will go next to the Senate for further consideration.

The Senate education committee is drafting a bill similar to the House measure and hopes to take action on it within weeks, said a Senate Democratic aide.

Democrats praised the House bill, saying it represents a victory for students over banks.

“Today the House made a clear choice to stop funneling vital taxpayer dollars through boardrooms and start sending them directly to dorm rooms,” said Democratic Representative George Miller, chief sponsor of the measure.

With six Republicans supporting the House measure on final passage, the White House claimed it as a bipartisan victory.

Some Republicans criticized the bill as a government takeover of an industry that has served students well.

“This bill is an expansion of the government ... a government takeover of an industry,” said Representative John Kline, the education committee’s top Republican.

“We see the passage of this legislation as being one of the key pillars of the president’s reform agenda being moved,” Melody Barnes, director of the White House Domestic Policy Council, said at a White House news briefing.

If approved by the Senate and signed into law, as expected, by President Barack Obama, the legislation would kill the 1970s-era Federal Family Education Loan Program (FFELP), the backbone of a once highly lucrative business model.

Enactment would also mark a step forward for the Obama administration in its broad effort to tighten regulation of banks and capital markets following the worst financial crisis in generations and in a nation mired in recession.

SALLIE SHARES SLUMP

Shares in Sallie Mae were down 1.5 percent to $9.10 in late New York Stock Exchange trading after the House vote. Just two years ago, the company’s stock traded for over $48 per share.

The fall of Sallie Mae’s share price has traced the decline of FFELP. For decades not only Sallie Mae, but many banks made big profits from FFELP subsidies they were paid by Washington to make cut-rate, government-guaranteed loans to students.

FFELP lenders were embarrassed by a 2007 scandal in which some were found to have given money and gifts to college financial aid officers to drum up business.

Then they took a heavy blow in mid-2008 when the secondary market for student loans froze up in a case of collateral damage from a credit crunch that shook economies worldwide.

The crisis left many U.S. students wondering if they would be able to pay for school in the 2008-2009 academic year and forced the government to mount a taxpayer-funded rescue.

That stabilized the market and produced a political opening for Democrats who had long wanted to kill FFELP.

Ending the program to protect students and stopping the subsidies it pays to lenders would save taxpayers some $80 billion over 10 years, said backers of the legislation.

Obama plugged the bill at a healthcare reform rally at the University of Maryland. “This plan would end the billions upon billions of dollars in unwarranted subsidies that we hand out to banks and financial institutions.” (Additional reporting by Thomas Ferraro and Patricia Zengerle, Editing by Kenneth Barry)