The budget will lay out how the president’s plans for spending over the next decade on infrastructure and social programs, such as paid family leave and universal preschool, will affect federal debt and deficits. Under the proposal, debt as a percentage of annual gross domestic product would within a few years exceed the level at the end of World War II and climb to 117% of GDP by the end of 2031, according to people familiar with the matter. That would be up from about 100% this year.

Administration officials have said that their proposals, known as the American Jobs Plan and the American Families Plan, would add to deficits over the next decade but that higher spending would eventually be offset by revenue from tax increases on wealthy individuals and corporations.

The president’s budget proposal serves as a fiscal blueprint for the administration’s policy priorities as well as signaling to Congress what the White House hopes to accomplish over the coming years. The proposal is generally seen as the opening salvo in a long process that leads to the government being funded, and lawmakers usually ignore the administration’s request in favor of their own plans.

President Biden’s budget plan would raise discretionary spending in fiscal year 2022 by 8.4%, or $118 billion, from the $1.4 trillion authorized last year, excluding emergency measures to combat the Covid-19 pandemic, according to a preliminary proposal released in April. Discretionary spending is the part of the budget that Congress shapes through the appropriations process.

Nondefense spending would rise 16% next fiscal year to $769.4 billion. Spending on defense would increase 1.7% to $753 billion—much less than what Republicans are likely to support but more than what has been called for by progressives, who pushed for cuts during the Trump administration.

The proposal fulfills some of Mr. Biden’s campaign promises, including more money for schools in high-poverty areas, cancer research and investments to address climate change.

Democrats in Congress welcomed the plan, saying it would provide money for long overdue investments after years of spending constraints. The details have drawn swift opposition from some Republican lawmakers, who have called it an intrusive expansion of federal power.

Republicans have criticized Mr. Biden for spending $1.9 trillion on the coronavirus-relief package, with trillions more proposed for infrastructure, education and child care. They have said Covid-19 aid is causing problems by fueling inflation and potentially giving people receiving unemployment benefits an incentive not to return to work.

“This is just a tax-and-spend administration on everything,” said

Sen. John Barrasso

(R., Wyo.). “They’re disconnected from reality.”

For the White House, the budget proposal reflects a broader shift in economic thinking that focuses on keeping interest payments on government debt in check rather than eliminating deficits over the next decade.

While overall debt would rise to the highest level ever, the administration expects net interest costs to hover around 2% of GDP for the next decade, which it sees as a prudent threshold.

When the pandemic hit last spring, widespread business closures triggered millions of layoffs that weighed on federal revenue, and Congress eventually authorized roughly $6 trillion in additional spending to cushion the economy. That sent deficits soaring, pushing federal debt to $21 trillion, roughly 100% of annual economic output.

Administration officials see higher deficits in the short term as helping bolster long-term growth, through spending on new programs that boost the economy’s productive capacity. By the end of the decade, deficits start to shrink under the president’s plan.

Write to Kate Davidson at kate.davidson@wsj.com