"I am pleased to announce that a deal has been struck with Senate Majority Leader Mitch McConnell, Senate Minority Leader Chuck Schumer, Speaker of the House Nancy Pelosi, and House Minority Leader Kevin McCarthy - on a two-year Budget and Debt Ceiling," the President said on Monday on Twitter, Xinhua news agency reported.
Trump, however, did not say whether he will sign the deal into law if it is passed in both chambers of Congress.
Earlier in the day, while hosting Pakistani Prime Minister Imran Khan in the Oval Office, Trump told reporters that "very good talks" on the issue were ongoing between administration officials and congressional leaders of both parties in both chambers of Congress.
"We're doing very well if you look at debt limit, however you want to define that," the president said. "And I think we're doing very well on the budget."
Citing people familiar with the talks, the US media reported on Monday that the agreement would raise overall spending levels by $320 billion for the next two years, compared to a limit set in a 2011 law.
The deal also will suspend the federal debt ceiling until July 31, 2021. The current debt ceiling expired on March 1, when the debt ballooned to over $22 trillion. The Treasury Department has taken a series of "extraordinary measures" to prevent the nation from defaulting on its payment obligations.
Packing the debt ceiling increase with an overall spending deal has been the request of House Democrats. Monday's deal also includes about $75 billion in offsets for equal increases in military and non-military spending.
While the Democrats succeeded in significantly lowering the offsets from the White House's original offer of $150 billion, Pelosi, a California Democrat, still faces liberals in her own caucus who oppose upping the defence spending. Trump said it was "very important" to take care of the US military.
In addition, the agreement will permanently end what is known as the "sequester," automatic across-the-board spending cuts required in the Budget Control Act of 2011. The sequester intends to cut spending for federal agencies totalling $1.2 trillion during the decade ending 2021, when the law is set to expire.
The legislative and executive branches must come up with short-term budget deals in order not to trigger the sequester, which did take effect in 2013 and has been avoided several times since. The current agreement, if reached, would avoid the return of the sequester in January.
A House vote is expected before Friday, when the chamber leaves for the August recess. The Senate's recess is scheduled to start on August 2.
( With inputs from IANS )