Both the S&P 500 and Nasdaq Composite surged into record territory at the opening bell, while the Dow also moved higher.
The S&P 500 has now set new intra-day highs for seven straight trading sessions.
"Today's jobs report was overall stronger but not strong enough to raise inflation and tightening concerns. It keeps the goldilocks scenario intact for stocks," said ThinkMarkets analyst Fawad Razaqzada.
The increase in jobs was better than the consensus forecast of economists and came after two months of disappointing results.
Investors have been concerned that too strong of an economic recovery could give the Federal Reserve further reason to begin cutting back or "tapering" its ultra-loose monetary policy.
Other data was less spectacular, with growth in average hourly earnings missing expectations.
The labour force only nudged higher, and remains some three million below its pre-pandemic peak.
"The key takeaway for the market is that it is apt to convince the Fed that it needs to take additional time to watch the incoming data before it moves to lessen its dovish-minded accommodation," said market analyst Patrick J. O'Hare at Briefing.com.
European markets also moved higher across the board following the US jobs data.
Asia was mixed as investors weighed the fact the Delta coronavirus variant has forced several governments, including Australia and South Africa, to reimpose lockdown measures.
Tokyo, Sydney, Singapore, Wellington, Manila, Mumbai and Jakarta were all up, while Seoul and Taipei were marginally lower.
Hong Kong and Shanghai tanked, however, following a recent run-up in the days leading into Thursday's Chinese Communist Party centenary celebrations, when authorities looked to provide support to markets.
However, other countries such as Britain, the United States and parts of Europe are pressing ahead with their reopenings despite a surge in new cases, with vaccines appearing to help keep deaths and hospitalisations down.
Johnson & Johnson became the latest pharma giant to say its drug was effective against Delta and offered durable protection against infection more broadly.
The International Monetary Fund added to the positive mood, on Thursday forecasting the US economy to expand seven percent this year, its highest growth since 1984, while it also upped its outlook for next year.
On oil markets, both main contracts dipped slightly following Thursday's rally that was fuelled by OPEC and other major producers delaying until Friday a decision on whether to boost output to meet surging demand. WTI and Brent are at levels not seen since 2018.
A panel had earlier recommended they pump an extra 400,000 barrels a day, less than forecast, despite fears that supplies are tightening quickly.
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