Bill Frist, the Senate Republican majority leader and Harry Reid, the leading Democrat in the Senate, said while some details still had to be worked out, they expected the Senate to pass a comprehensive reform package shortly.
Frist, at a news conference with Reid and a dozen other Republicans and Democrats, said: "We've had a huge breakthrough ... that will lead us to the conclusion of passing a very important bill."
The deal centres on a compromise offered by Republicans that included a temporary worker programme backed by George Bush, the president.
It also would allow illegal immigrants who have been in the US for more than five years a chance to become citizens, if they meet a series of requirements - including registering for military service - and pay a fine.
Bush, who has been pushing for comprehensive changes, said he was encouraged by the breakthrough and urged quick passage of the legislation that has sparked mass protests.
"I recognise there are still details to be worked out," Bush said. "I would encourage the members to work hard to get a bill done prior to the upcoming break."
"We've had a huge breakthrough ... that will lead us to the conclusion of passing a very important bill"
Senate Republican leader
The measure still faced opposition from some Republicans who said the bill would give amnesty to people who broke the law.
Five Senate Republicans - John Cornyn, Jeff Sessions, Jon Kyl, Saxby Chambliss and Johnny Isakson - announced their opposition.
They said, however, that they did not know if they could muster the needed 41 votes in the 100-member Senate to stop the bill with a procedural block.
The Senate compromise would also allow illegal immigrants who had been in the US less than five years but more than two years, to apply for a work visa. But they would have to travel to a US port of entry and step outside the country to get it.
Any Senate bill would have to be merged with legislation passed by the US House of Representatives that focuses only on border security and enforcement of immigration laws.
Senators said that details of the
bill still had to be worked out
That bill would make it a crime, instead of a civil offence, to be in the country illegally and calls for the construction of a fence along parts of the US border with Mexico.
That bill angered Hispanics and their supporters and sparked protests around the country. Nationwide demonstrations also were planned for Monday.
Reid said lawmakers where happy to get a deal that will help millions of people who are living and working in the US, many in low-paying jobs.
"Even though we all feel good about today, it pales in comparison to the millions and millions of people out there who today feel that they have a chance to participate in the American dream," he said.