The House on Thursday voted 305-102 in favour of the Senate measure, which differs significantly from the border legislation passed earlier by the lower chamber, reports Efe news.
Democratic leaders, after initially rejecting the idea of accepting the Senate version, decided to over-rule objections from their own progressive members and pass the bill with the expectation that President Donald Trump would sign it.
House Speaker Nancy Pelosi agreed to push the Senate bill with an eye toward ensuring that emergency funding to address the crisis on the border would not be delayed until after the congressional recess for the July 4th holiday.
The bill includes $3 billion for humanitarian aid to improve conditions for undocumented migrants in detention.
But the Senate measure also features provisions opposed by progressive Democrats in the House, such as more money for the Defence Department and funds to pay overtime to Immigration and Customs Enforcement personnel.
Another provision of the House bill would have required Customs and Border Protection to enact health and hygiene standards for individuals in custody - a response to recent revelations about squalid conditions at facilities where minors are being held.
The House draft was defeated 55-37 in the Senate and Trump had threatened to veto the Democratic legislation.
The usual practice in these situations is for senators and representatives to meet in conference and reconcile the rival bills, but Republican and Democratic leaders indicated they had no plans to go that route.
Senator John Thune of South Dakota, the second-ranking Republican in the Senate, said on Wednesday that going to conference wasn't a "viable" option.
"The House knows that they can't get a signature on their bill, and most of what they want is in our bill and ours is a bipartisan bill," he said.
Democrats, meanwhile, said they would only accept the Senate bill if Republicans agreed to make some changes.
"They passed their bill, we respect that. We passed our bill, we hope they will respect that," Pelosi said 24 hours before endorsing the Senate legislation.
More than 132,000 undocumented migrants were detained on the southern border in May, the highest one-month total since 2006.
( With inputs from IANS )