The agreement would keep federal operations running through September 30, the end of the fiscal year.
Congress is expected to vote in the coming days on the package, which aides said includes some $1.5 billion in funding for increased border security measures, but no funding for an actual wall.
They also said it adds $2 billion in new funding for the National Institutes of Health, and is expected to increase military spending.
Comprehensive details were not available Sunday as the measure had yet to be officially finalized and released. Lawmakers have until Friday to get new spending legislation to President Donald Trump's desk.
"This agreement is a good agreement for the American people, and takes the threat of a government shutdown off the table," Senate Minority Leader Chuck Schumer said in a statement.
"The bill ensures taxpayer dollars aren't used to fund an ineffective border wall, excludes poison pill riders, and increases investments in programs that the middle-class relies on, like medical research, education, and infrastructure."
Trump made building the wall one of the primary pledges of his presidential campaign, insisting it would begin within his first 100 days, a milestone that came and went on Saturday.
Last week White House aides acknowledged the administration could wait until later this year or next year to consider funding for the wall.
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