President Donald Trump on Wednesday hailed the adoption of a sweeping Republican tax cut plan as a "historic victory" for the American people.

The U.S. leader got his first major legislative win, with lawmakers giving final approval to the most sweeping tax cuts in a generation.

"We had a historic victory for the American people," Trump told reporters in a celebratory address from the White House Cabinet Room.

"We got it done," he added, thanking the Republican leaders in Congress, Mitch McConnell and Paul Ryan, by name. "We have a tremendous amount of talent."

McConnell, the Republican Senate leader, responded by saying the bill's passage caps a year of "extraordinary accomplishment" for Trump, while House Speaker Ryan praised Trump's "exquisite presidential leadership."

At the event, Trump also invited his Housing and Urban Development Secretary Ben Carson to say a prayer for the assembled reporters and cabinet members -- during which Carson notably cited concerns about the national debt.

Eyeing the most important legislative victory in the 11 months since his inauguration -- after the stinging failure to repeal his predecessor's health care law -- Trump has demanded the bill reach his desk by Christmas.

The Senate passed the Republican bill in the wee hours and the House -- which already approved it on Tuesday -- was scheduled for a technical re-vote on the $1.5 trillion due to a procedural snag.

The deepest rewrite of the U.S. tax code in three decades provides dramatic tax breaks to corporations, and families at all income levels will see their tax drop -- in what Republicans hope will play to their advantage in next year's mid-term elections.

The tax plan also takes a key step towards dismantling Barack Obama's health reforms, by scrapping the individual mandate that requires nearly all Americans to have health insurance or pay a fine.

"We have essentially repealed Obamacare and we will come up with something much better," Trump declared.

Earlier Trump had tweeted out his praise for Senate Majority leader McConnell, congratulating him on a "fantastic job both strategically & politically on the passing in the Senate of the MASSIVE TAX CUT & Reform Bill."

"I could have not asked for a better or more talented partner. Our team will go onto many more VICTORIES!"