The Standard and Poor's 500 index tipped beyond 1,000 for the first time since November and the Nasdaq hit above 2,000 - the first time since October.
The three major US indexes all added 1.25% or more by close of trade after a manufacturing survey rose in July.
European indexes rose with London's FTSE closing at its highest since October and the pound rising.
France's Cac 40 rose 1.5% and Germany's Dax added 1.78%
'Growth expectations'
World markets took heart after brighter UK economic data and a rally in financial stocks following profits from banking giants HSBC and Barclays.
Later in the day the US Institute of Supply Management said its index of manufacturing activity reached a reading of 48.9 last month from June's reading of 44.8 - beating expectations.
"We're past the worst of it on the manufacturing side, and we could even be getting back to growth by the third quarter of this year," said Jill Evans, co-portfolio manager, Alpine Dynamic Dividend Fund.
Ryan Sweet at Moody's Economy.com said the results were "consistent with our forecast for both manufacturing and (the overall economy) to rebound this quarter."
Analysts think investors are accepting the idea that the economy could be over the worst and a recovery better than has been previously thought.
"The shift in growth expectations that has occurred during the last two weeks has occurred with the subtlety of a sledge hammer," said Kent Engelke at Capitol Securities Management.
Risers in the US included Ford, which added more than 4% after seeing sales climb 2.3% in July from a year earlier.
Also higher was Apple, boosted after Google chief Eric Schmidt left Apple's board of directors because of conflict of interest concerns.
And safe-haven investments including Treasuries and the US dollar fell, while more volatile stocks - such as oil and other commodities - climbed.
The price of sweet crude added $2.13 to settle at $71.58 a barrel on New York's Mercantile Exchange.
Optimism
Sterling rose as high as $1.6965 against the dollar and hit a one-month high against the euro of 84.63p.
The FTSE 100 index ended at its highest level since early October, soon after Lehman Brothers collapsed, at 4,682.46. Earlier it reached an intra-day trading high of 4,710.23.
Shares in Barclays climbed 6.7% after reporting an 8% rise in half-year profits, while HSBC rose 5% after it made better-than-expected profits of $5bn.
Oil prices also rose to a one-month high above $71 a barrel, as an economic recovery should lead to greater demand for crude.
Lift for pound
The pound got a lift after data showed the UK manufacturing sector expanded for the first time in more than a year.
Manufacturing activity rose last month for the first time since March 2008, as new orders came in, according to a survey by the Chartered Institute of Purchasing and Supply (CIPS) and Markit.
"The manufacturing sector has clearly pulled out of the nosedive it was in earlier this year and is no longer plummeting," said David Noble, chief executive of CIPS.
While still a long way below the $2 levels seen in July last year, the pound has rebounded 25% from the 23-year low of $1.35 it hit in January this year.
"Over the medium-term we are forecasting for sterling to continue to gain against the greenback, particularly if banks and blue-chip stocks show renewed strength, as Barclays did today," said David Clements, senior analyst at Caxton FX.
The UK economy is viewed as being particularly reliant on the banking sector so evidence of any upturn benefits sterling.
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