The House on Tuesday voted 237-187 in favour of the Dream and Promise Act of 2019, as seven Republicans joined the Democrats in supporting the measure, the Hill magazine reported.
The largest contingent of potential beneficiaries comprises the more than 700,000 undocumented youth who enjoy protection from deportation under the Deferred Action for Childhood Arrivals (DACA) initiative, known as Dreamers.
DACA began in 2012 under then-President Barack Obama.
The bill would grant permanent residency with a path to citizenship to over 2 million immigrants across three categories: It would permanently protect Dreamers - immigrants who came to the country illegally as children - as well as certain recipients of the Temporary Protected Status (TPS) and Deferred Enforced Departure (DED) programmes from deportation.
TPS and DED are programmes that grant work permits and protect from deportation citizens of certain countries have undergone natural or man-made disasters.
The bill's supporters cheered its passage, as immigration advocates had been trying to pass elements of the bill for the better part of two decades.
Still, it's unlikely the bill will see a vote in the GOP-led Senate as the White House "strongly opposed" the measure.
President Donald Trump announced in 2017 that he would scrap DACA on March 5, 2018, if Congress could not come up with a permanent legislative fix to resolve the issue of the Dreamers.
But the deadline came and went and DACA remains in effect, thanks to federal court decisions preventing the administration from ending the programme.
( With inputs from IANS )