The S&P 500 index climbed 18.62 points, or 0.86%, to 2,182.87, beating an all-time high record set last month.
The Dow Jones Industrial Average rose 191.48 (1.04%) to 18,543.53, while theNasdaq was up 54.87 (1.06%) to 5,221.12.
The US economy added 255,000 jobs last month and figures for May and June were also revised upwards.
The figures add to speculation that the Federal Reserve will raise interest rates by the end of the year.
“The most important takeaway from a better jobs report is an indication of a continued grind higher in the US economy,” said Michael James, managing director of equity trading at Wedbush Securities.
Shares in banks, which are expected to gain from any rise in interest rates, were higher. Goldman Sachs climbed 2.6% and JP Morgan Chase rose 2.7%.
Shares in Bristol-Myers Squibb sank 16% after the company said its Opdivo cancer treatment had failed in a key study.
In contrast, shares in Merck, which makes a rival treatment, saw its shares jump 10% to $63.86.
On the Nasdaq, shares in Google’s parent company, Alphabet climbed 1.2%, whileApple stock jumped 1.5%.