The measure would affect so-called "527 groups" which have seized on a once-obscure section of the tax code to conduct unlimited political activity without reporting anything about themselves to the public.
"I look forward to signing it as a first step toward meaningful campaign finance reform," President Clinton said in a statement Thursday afternoon.
It was the first major victory for campaign finance reformers in 20 years, reports CBS News Correspondent Bob Fuss, and it came over the objections of some powerful congressional Republicans, including House Whip Tom DeLay of Texas, who hoped to use 527s to raise $25 million for upcoming GOP campaigns.
Backers vowed to build on the overwhelming vote to pass other campaign finance legislation.
"Today is only the first step," said Sen. John McCain, R-Ariz., who built a presidential bid around his campaign for finance reform. "It is indeed a great day for democracy."
"It is not an attempt to silence anyone. It is an attempt to give the American people information," said Sen. Russell Feingold, D-Wis.
Sen. Mitch McConnell, R-Ky., who leads the Senate's opposition to campaign finance overhaul, was one of a handful senators to vote against the disclosure bill.
He said that while the legislation would not put Republicans at a disadvantage in the fall elections, it is "arguably unconstitutional" because it requires disclosure of donors who pay for "issue ads," which stop short of telling people who to vote for, though they look just like regular campaign commercials.
Many interest groups that are not covered by the legislation run these types of ads as well, and they, too, do not disclose their donors.
"Nevertheless, I'd say to my Republican colleagues, particularly those up for re-election, that's pretty hard to explain," McConnell said.
"I do not think this is a spear worth falling on four months before an election."
He suggested groups affected by the bill would either disband or fight the measure in court.
The legislation would require tax-exempt groups that register under the newly popular section 527 of the tax code to say who is paying for their political activities, including TV ads and other attempts to influence elections.
Section 527 has been in the tax code since 1975, but only recently has it become the vehicle of choice for donors who want to remain anonymous.
Using a 527, a pair of Texas brothers ran $2.5 million in ads praising Texas Gov. George W. Bush and attacking McCain in the days before a crucial GOP primary election.
One of the oldest 527s is the Sierra Club, which is running an $8 millon campaign boosting Democrats running for Congress and attacking Bush's record in Texas.
The bill would take effect the day Mr. Clinton signs it. Groups will not have to reveal donations made before then.