The ride-hailing taxi app firm has priced its shares at $45 (£35). The deal values Uber at $82bn (£63bn).
The price is near the bottom of the expected $44-$50 range - a sign that investors are cautious about the firm.
Uber hopes to sell 180 million shares when trading starts on Friday.
This is the highest profile US flotation since Facebook seven years ago, analysts say.
Rival Lyft's flotation was priced at $72 per share when it listed on the New York Stock Exchange in March, but its share price has fallen by as much as a third since then.
Uber is keen to avoid a similar fate, but the firm has so far failed to make a profit, and has warned that it might never do so.
Continuous losses
Uber, which started in 2009, was most recently valued at $76bn in the private market. It had been seeking a valuation as high as $120bn.
As well as the original "ride-hailing" business, Uber is developing driverless cars, and has a food delivery operation, Uber Eats.
In 2018, Uber saw a 24% increase in revenues and a 37% rise in gross bookings, but its adjusted loss - following a tax benefit - still hit $1.8bn.
In the first three months of 2019, Uber drivers made 1.5 billion passenger journeys, but the firm reported a net loss of about $1bn.
Lyft is also yet to make a profit - it reported widening losses of $911m last year, compared with $688m in 2017, despite revenues rising to $2.1bn.
