Official data showed the US economy added 209,000 jobs last month, beating analysts' expectations, while the unemployment rate fell to 4.3%.
The Dow Jones closed at a record for the eighth consecutive day, rising 0.3% to 22,092.81.
The wider S&P 500 index closed up 0.19% at 2,476.83, while the Nasdaq rose 0.18% to 6,351.56.
Analysts said the latest jobs report meant the Federal Reserve was still on track to raise interest rates later this year, which would be the third increase in 2017.
Shares of banks, which benefit from higher rates, saw some of the most significant gains on Friday. Goldman Sachs was among the biggest winners on the Dow, rising 2.6%.
Among individual stocks, Viacom shares sank nearly 14% after it forecast a drop in sales to US pay-TV companies and streaming services in the current quarter.
Consumer review website operator Yelp saw its shares jump by more than a quarter after it announced the sale of its Eat24 business to Grubhub for $287.5m.
Yelp also reported revenues of $209m for the second quarter of the year, which beat analysts' expectations.
US stocks are in record territory this year. The Nasdaq is up almost 17% since January. The Dow has risen 11% and the S&P 500 is climbed almost 10%.
Stronger than expected jobs figures helped to lift US stocks on Friday, leading the Dow to another record.