"We have an agreement in principle," Rep. John Carter, R-Texas, said after he and other members of the so-called Gang of Eight ended a 2-hour meeting over submarine sandwiches late Thursday.
Democrats confirmed the stepping-stone deal.
The lawmakers said the Republican-controlled House planned to work out the details next week and begin drafting it as legislation before taking a Memorial Day break and introducing the bill June 4.
Details of the compromise were not released, but one House group member told ABC News Rep. Raul Labrador, R-Idaho, was the last holdout.
He wasn't present but called in from Idaho, where his daughter had a recital, and eventually agreed to a deal when language proposed by Democrats made clear taxpayer money would not pay for immigrant healthcare, the member said.
The eventual House bill is expected to be similar to one introduced in the Democratic-controlled Senate, including a path to legalization for the 11 million workers currently living in the United States without legal permission, as well as increased border security measures.
But aides told The New York Times the House version would most likely call for a 15-year path to citizenship, rather than the Senate's 13-year path. It would also likely require people living in the country illegally to sign an admission they violated U.S. immigration laws, the aides said.
House Speaker John Boehner, R-Ohio, told reporters earlier Thursday he was "concerned that the bipartisan group has been unable to wrap up their work."
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