At the close of U.S. trading, the Dow Jones Industrial Average finished up 0.96%, the S&P 500 index rose 1.05%, while the Nasdaq Composite index rose 1.14%.
The Bureau of Labor Statistics reported earlier that the U.S. economy added 165,000 nonfarm payrolls in April, up from 138,000 in March, whose figure was revised up from 88,000.
April's figures far outpaced analysts' forecasts for a 145,000 figure, while February's figures were revised to 332,000 from 268,000.
The headline unemployment rate ticked down to 7.5% in April from 7.6% in March.
The numbers fueled demand for risk-on asset classes such as stocks, which enticed investors out of the safety of the dollar and sparked a rally on Wall Street
Elsewhere, the Institute for Supply Management reported that its April non-manufacturing index fell to 53.1 in April from 54.4 in March, missing market calls for a 54.0 reading, the slowest pace of expansion since July of last year.
Still, a reading over 50 indicates expansion, which gave stocks further room to rise.
Leading Dow Jones Industrial Average performers included Caterpillar, up 3.24%, Alcoa, up 2.01%, and Boeing, up 1.67%.
The Dow Jones Industrial Average's worst performers included Pfizer, down 1.09%, JPMorgan & Chase, down 1.04%, and UnitedHealth Group, down 0.94%.
European indices, meanwhile, finished higher.
After the close of European trade, the EURO STOXX 50 rose 1.65%, France's CAC 40 rose 1.40%, while Germany's DAX 30 finished up 2.02%. Meanwhile, in the U.K. the FTSE 100 finished up 0.94%.