The bill must still pass the House of Representatives as well as the Senate. The deal would also reopen the government, which has been partially shut for 16 days.
The Standard & Poor's 500 index gained 21 points, or 1.3 percent, to 1,719, just six points from its all-time high of 1,725 set Sept. 18.
The Nasdaq composite rose 43 points, or 1.2 percent, to 3,834.
Unless the debt limit is raised, the U.S. will hit a Thursday deadline after which it can no longer borrow money to pay its bills, increasing the chance of a default on government debt. That possibility has unnerved markets all month.
"The lawmakers know it's in our best interest for this to be settled," said JJ Kinahan, chief derivatives strategists for TD Ameritrade. "There's a belief that they'll take it as far as they can and ultimately, at the last minute, settle it."
Yields on Treasury bills fell sharply as hopes built for compromise ahead of the Thursday deadline to raise the U.S. debt ceiling. The yield on the one-month T-bill dropped to 0.26 percent from 0.40 percent earlier Wednesday morning, an extraordinarily large move. The decline means that investors consider the bill to be less risky.
The yield on the 10-year bond edged down to 2.72 percent from 2.74 percent Tuesday. Yields on longer-term U.S. government debt haven't moved as much as those on short-term debt because investors generally believe the government will work out a longer-term solution for paying its debts on time even as partisan gridlock in Washington holds up a short-term solution.
Fitch Ratings said late Tuesday that it may downgrade the government's AAA bond rating. The agency said it sees a higher risk for default because of the uncertainty over whether Congress will raise the debt limit. Fitch said it will make a final decision by the end of March at the latest, depending on how long any agreement to raise the debt ceiling lasts.
Unlike previous government-induced sell-offs in recent years, stock investors have stayed largely calm throughout the latest twists in the current fiscal saga in Washington. Even before Wednesday's news, the S&P 500 and the Dow were up for the month.
In the summer of 2011, the index plunged 17 percent between early July and early August as lawmakers argued over raising the debt limit and Standard & Poor's cut the U.S. credit rating from 'AAA,' its highest ranking.
Stocks also slumped in the last two weeks of 2012 as investors fretted that the U.S. would go over the "fiscal cliff" as lawmakers argued over a series of automatic government spending cuts.
"Investors have become, unfortunately, accustomed to some of the dysfunction," said Eric Wiegand, a senior portfolio manager at U.S. Bank. "It's become more the norm than the exception."
Instead, investors are focusing on Federal Reserve's decision to maintain its economic stimulus program, steady growth in earnings at U.S. companies and the prospect of better global economic growth.
Among stocks making big moves:
— Mattel gained $1.75, or 2.2 percent, to $43.30, after the company's third-quarter net income rose 16 percent thanks to high demand for dolls like Monster High, Barbie and American Girl. The results were better than Wall Street analysts had forecast.
— Bank of America rose 22 cents, or 1.5 percent, to $14.46 after the second-largest U.S. bank reported that it earned $2.5 billion in the July-September period, up from $340 million a year earlier. On a per-share basis, earnings were 20 cents, beating the 19 cents expected by financial analysts.
— Stanley Black & Decker plunged $12.60, or 14.1 percent, to $76.68 after the company lowered its profit forecast for the year, citing slower growth in emerging markets and a hit from the U.S. government shutdown.