As outlined, the measure would provide for enhanced border security, regulate the future flow of immigrants into the United States and offer legalized status to the millions of men, women and children in the country unlawfully.
"We've had a huge breakthrough ... that will lead us to the conclusion of passing a very important bill," Majority Leader Bill Frist, R-Tenn., said.
Sen. Harry Reid of Nevada, the Democratic leader, agreed, but cautioned that the agreement had not yet been sealed.
Even so, the presence of both leaders at a celebratory news conference underlined the expectation that the Senate could pass the most sweeping immigration bill in two decades, and act before leaving on a long vacation at the end of the week.
President Bush wasted no time encouraging the Senate to keep moving on the immigration issue.
"I am pleased that Republicans and Democrats are working together on a comprehensive immigration bill," he told reporters as he wrapped up a North Carolina visit.
The Senate action is good news, at least in the short term, for the president, reports CBS News White House correspondent Peter Maer. It points to reforms he wants, including a guest worker program and tougher border controls.
Assuming the Senate irons out remaining details and gets this passed, an immigration bill is still a very long way from becoming law. That's because the bill passed in the House is dramatically different, CBS News correspondent Bob Fuss reports. It declares all illegal immigrants to be felons, seeks to punish anyone who helps them in any way and orders a huge fence built along the Mexican border. Finding common ground with a Senate bill to legalize most illegal immigrants won't be easy.
The White House sees months of negotiation ahead, with no final action expected until after the November elections, Maer reports.
The developments marked a turnaround from Wednesday, when it appeared negotiations had faltered. The key sticking point involved the 11 million illegal immigrants in the country, and the struggle to provide them an opportunity to gain legal status without exposing lawmakers to the political charge that they were advocating amnesty for lawbreakers.
While final details were not available, in general, the compromise would require illegal immigrants who have been in the United States between two years and five years to return to their home country briefly, then re-enter as temporary workers. They could then begin a process of seeking citizenship.
Illegal immigrants here longer than five years would not be required to return home; those in the country less than two years would be required to leave without assurances of returning, and take their place in line with others seeking entry papers.
Sen. Ted Kennedy, D-Mass., who led the bipartisan push for an immigration bill with Republican John McCain, hailed the compromise. Kennedy said the new bill "will send a very clear message to a very important group of individuals that are here. And that is, that if you work hard, you're devoted to your family, you play by the rules, you pay your taxes and you work toward the American dream, that you can be included, too."
Republican Sen. Lindsey Graham of South Carolina called the deal "a plea bargain with 11 million illegal aliens. ... For those out there who want people to pay a price for breaking the law, you pay a price. For those out there who want 11 million people to come out of the shadows and earn their right to be part of the American family, you have also been satisfied."
Beyond the illegal immigrants, there were other thorny issues to be clarified. Senate leaders had yet to publicly unveil draft legislation to make sure that only legal workers were hired in the future, for example.
Nor was it clear what type of assurances, if any, Democrats had received from the White House and Republicans about compromise talks with the Republican-controlled House later this year. The House has approved legislation limited to border security, and while GOP leaders have signaled support for a broader measure, Democrats have expressed concern in recent days that they will be pressured to make unacceptable additional concessions to achieve a final compromise.
But not everyone was satisfied. "I'm not impressed," said Sen. Jeff Sessions, who has criticized earlier versions of the measure as too lenient on lawbreakers. Sens. John Cornyn and Jon Kyl joined him in criticizing the measure, as did Republicans Saxby Chambliss and Johnny Isakson.