The $1.6tn (£1.2tn) figure includes $886bn for defence and more than $704bn for non-defence spending, according to Republican House Speaker Mike Johnson.
However, there appears to be some discrepancy over the numbers.
The deal now needs approval from the House of Representatives and Senate.
They have less than two weeks to finalise funding and stop the suspension of some federal services.
According to a statement from Democrats Hakeem Jeffries and Chuck Schumer - House Minority Leader and Senate Majority Leader respectively - the non-defence spending amount agreed is $772bn.
Mr Johnson, announcing the deal had been reached in a letter to colleagues, accepted that the amount of funding "will not satisfy everyone, and they do not cut as much spending as many of us would like."
Republicans have been seeking to freeze overall government spending by cutting some budgets.
Sunday's deal includes greater protection from cuts to benefits and health - a provision demanded by Democrats.
The House Freedom Caucus, a conservative Republican group within Congress, called the deal a "total failure".
"Sad to say but the spending epidemic in Washington continues with both parties being culpable," said Andy Biggs, the group's former chairman.
In a statement, Mr Jeffries and Mr Schumer said the agreement "clears the way for Congress to act over the next few weeks in order to maintain important funding priorities for the American people and avoid a government shutdown".
President Biden, meanwhile, said it "moves us one step closer to preventing a needless government shutdown and protecting important national priorities".
Lawmakers are due to resume negotiations in Washington on Monday following the holiday break and have until 19 January to sort out funding for programmes including transport, housing and energy.
A second load of annual funding, for sectors including defence, expires on 2 February.The agreement on an overall amount of spending comes after the government in October secured a short-term deal to avoid a federal shutdown temporarily, which was signed into law by President Joe Biden minutes before the deadline.
Shutdowns normally happen when both chambers of Congress are unable to agree on the roughly 30% of federal spending they must approve before the start of each fiscal year on 1 October.
With Republicans holding a slim majority in the House and Democrats holding the Senate by a single seat, any funding measure needs buy-in from both parties.
Repeated efforts to pass spending bills in the House in recent months have been thwarted in recent weeks by rebel right-wing Republicans.
Meanwhile, an agreement has still not been reached on a separate bill which includes a further $50bn of military aid to Ukraine, as Congress continues to argue over migration policy at America's southern border.
October's short-term deal to prevent a shutdown excluded new aid for Kyiv in a blow for Democrats, for whom this was a key demand.
Some Republicans argue that any further funding would be detrimental to America's interests.
Congress has so far approved more than $100bn (£78bn) in military, humanitarian and economic aid to Ukraine since Russia began its full-scale invasion last year.
Negotiations are also continuing about providing further security aid to Israel as it seeks to eliminate Hamas following the 7 October attacks.