Summers' surprise decision on Sunday came two days before the US central bank will meet to decide when and by how much to scale back its bond purchases from the current pace of $85 billion a month.
S&P 500 futures rose 16.5 points and were above fair value, a formula that evaluates pricing by taking into account interest rates, dividends and time to expiration on the contract. Dow Jones industrial average futures rose 167 points, and Nasdaq 100 futures added 25.3 points.
"Stock index futures have reached a record high - although the cash market still has some work to do - as investors warm to a late Summers rally," said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co in New York.
"His passing as a contender for the top role has left in its wake a significant risk-on rally."
Treasuries prices and European shares rose while the dollar fell near a four-week low against other major currencies on the news.
Of the two leading candidates for the Fed chairmanship, Summers was regarded as more eager to scale back the Fed's $85 million a month bond buying. Janet Yellen, the Fed's vice chairwoman and the other leading candidate to succeed Fed chief Ben Bernanke. Yellen is perceived as favoring a more gradual easing of stimulus to accelerate the lowering of the unemployment rate.
The gains in futures come after the Dow Jones industrial average on Friday registered its best weekly gain since January, though trading was subdued before the Fed's meeting, which is expected to result in the start of tapering.
Further whetting risk appetite, the United States reached a deal with Assad's ally, Russia, on chemical weapons that could avert US strikes on Syria.
In economic news, the pace of growth in New York state's manufacturing sector unexpectedly slowed this month, but firms' outlook brightened. Market reaction was muted.
In company news, Saudi billionaire Prince Alwaleed bin Talal says he will not sell any of his shares in microblogging site Twitter Inc when it goes public, and expects the firm's IPO to hit the market later this year or in early 2014.
A handful of potential bidders, including private equity firms, are lining up to look at BlackBerry Ltd , but initial indications suggest that interest is tepid and buyers are eyeing parts of the Canadian smartphone maker rather than the whole company, several sources familiar with the situation said.
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