The vote was 81-18, with 17 Democrats voting against the measure, which now goes back to the House, The Hill reported.
President Obama said he would sign the bill if it reaches his desk in its present form.
"A better bargain for the middle class means making a college education available to every single American willing to work for it," Obama said in a statement released by the White House after the Senate vote. "That's why I applaud the wide bipartisan majority of senators who passed a bill to cut rates on nearly all new federal student loans, rolling back a July 1 rate hike and saving undergraduates an average of more than $1,500 on loans they take out this year.
"This compromise is a major victory for our nation's students. It meets the key principles I laid out from the start: It locks in low rates next year, and it doesn't overcharge students to pay down the deficit.
"I urge the House to pass this bill so that I can sign it into law right away, and I hope both parties build on this progress by taking even more steps to bring down soaring costs and keep a good education -- a cornerstone of what it means to be middle class -- within reach for working families."
Need-based student loan rates doubled from 3.4 percent to 6.8 percent July 1. Sen. Dick Durbin, D-Ill., said under the Senate version, the rate will drop to 3.8 percent.
"This agreement will ensure students loan rates will fall below the 6.8 percent rate that kicked in on July 1," said Durbin after the vote. "Once again we've shown that when both sides work together, we can reach fair and bipartisan solutions to some of the nation's biggest issues. Now that we've found a way to keep student loan rates low, I hope we can return to a more basic conversation about the underlying and unsustainable cost of education in America."
Sen. Elizabeth Warren, D-Mass., one of those who voted against the bill, said she couldn't stomach seeing student loans interest rates that could still go as high as 8.25 percent over time.
"I cannot support a plan that raises interest rates in the long-term while the federal government profits off them," The Hill quoted Warren as saying. "This is obscene. Students should not be used to generate profits for the government."
Since the Senate amended the House's Smarter Solutions for Students Act, the lower body must take it up again and likely will do so before its August recess, the Washington publication said.