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Nonfarm payrolls increased by 223,000 in April, just below the 224,000 that economists polled by Reuters had expected.
The unemployment rate dropped from 5.5 percent to 5.4 percent, its lowest level since May 2008, despite an increase in the number of people entering the labor market.
The drop in the unemployment rate pushed it to within a whisker of the 5.0 percent to 5.2 percent range that most Fed officials consider consistent with full employment.
"I think this is exactly what the market was looking for. It's a Goldilocks number - not too strong, not too weak," said Adam Sarhan, chief executive of Sarhan Capital in New York.
March payrolls were revised to show only 85,000 jobs created, the smallest since June 2012.
Still, the solid report suggested underlying strength in the economy at the start of the second quarter after growth hit a soft patch in the first.
"As it relates to the next Fed move, it would seem June is definitely off the table and looking at September will probably be when it will happen," said Erik Davidson, chief investment officer at Wells Fargo Private Bank in San Francisco.
At 9:41 a.m. ET (1341 GMT) the Dow Jones industrial average rose 219.01 points, or 1.22 percent, to 18,143.07, the S&P 500 gained 21.39 points, or 1.02 percent, to 2,109.39 and the Nasdaq Composite added 49.48 points, or 1 percent, to 4,995.02.
All 30 Dow components were higher, while all the 10 major S&P 500 sectors notched strong gains, with the utilities and health rising 1.3 percent.
Microsoft jumped 2.7 percent to $47.95 and gave the biggest boost to the S&P and the Nasdaq after Reuters reported that the company was currently not weighing an offer for Salesforce.com. Salesforce.com fell 2.2 percent to $72.86.
McDonald's rose 1.4 percent to $98.11 after it reported a lower-than-expected fall in worldwide sales at its established restaurants in April.
AOL jumped 8.9 percent to $42.90 after reporting revenue above analysts' expectations.
Monster Beverages slid 5.6 percent to $135.26 as one of the best performing U.S. stocks over the past decade posted a rare results miss.
Advancing issues outnumbered decliners on the NYSE by 2,331 to 453, for a 5.15-to-1 ratio on the upside; on the Nasdaq, 1,763 issues rose and 545 fell for a 3.23-to-1 ratio favoring advancers.
The benchmark S&P 500 index was showing 12 new 52-week highs and one new low; the Nasdaq showed 37 new highs and 14 new lows.
