The bill would also allow hundreds of thousands of Temporary Protected Status (TPS) recipients - as well as Liberian immigrants covered by Deferred Enforced Departure (DED) - to gain permanent residency.
While Democrats secured the bill's passage in the House, the measure is unlikely to become law anytime soon, particularly ahead of a presidential election.
The bill is not expected to pass in the GOP-led Senate.
Tuesday's passage is a success for Democrats, particularly after a federal judge in Washington a day earlier denied a request by House Democrats to block Trump from transferring funds from appropriated accounts to construct his wall.
Several thousand Liberians fleeing violence and the Ebola virus who've won temporary legal status in the US would also be given a chance for permanent residence and citizenship.
It also provides some $3 billion to farmers who lost crops due to natural disasters.
The bill - dubbed the Dream and Promise Act, H.R. 6 (116) - was approved, 237-187, along largely partisan lines. Among the bill's supporters are the US Chamber of Commerce, the AFL-CIO labour organisation, immigration and liberal groups.
Arizona helicopter rescue gurney carrying woman, 74, spins uncontrollably midair
The video of her chopper rescue was shared widely online after netizens noticed her stretcher spun rapidly while being pulled up. It wasn't until the helicopter began to fly away from its stationary position that the harsh motions started to subside.
"That is a great thing, to give these young people who came here through no choice of their own, the maximum opportunities for success", said Stanton, who later described the measure as "an economic stimulus bill".
According to CNN, the vote comes almost a month after Trump introduced a plan to overhaul the country's immigration system. Senate Majority Leader Mitch McConnell (R., Ky.) indicated Wednesday that any amnesty deal would need to come with substantive fixes to border security.
"Today, we are rejecting the political stunts and grandstanding that have made it hard to deliver much-needed disaster relief to families and communities across America", Appropriations Committee Chairwoman Nita Lowey of NY said on the House floor. They also have to have lived continuously in this country for four years, have a diploma from a USA high school or a GED.
The Senate cleared the package last Thursday, after months of protracted negotiations and disputes between lawmakers and the Trump administration over aid to Puerto Rico and funding for border security and immigration.
"Because of Donald Trump's anti-immigrant policies, millions of immigrants across the country live in constant fear that they will face deportation and potentially be separated from their families", Velázquez said.
"I think we could do better", Shelby said.
"I will certainly use my voice to beat the drum and push senators like Marco Rubio to get behind these measures", she said, referring to the Florida Republican who has supported immigration bills in the past and has a large population of protected Haitians and Central Americans in his state.