That is above the $23 to $25 range announced on Monday and values the short messaging service at more than $18 billion.
That makes it the biggest market debut for a technology firm since Facebook went public in May 2012.
Twitter has attracted 230 million users since starting seven years ago, but is yet to make a profit.
Its losses for Q3 2013 increased to $64.6 million, from $21.6 million a year earlier and a recent poll by Reuters/Ipsos showed that more than a third of registered users do not use the service at all.
Nevertheless there was strong demand for the shares and the company was able to raise the offering price twice.
Twitter has posted an increase in its sales, which more than doubled in Q3 to $168.6 million, and it is looking to raise even more revenue from advertisers outside the US.
Its $18 billion valuation includes the value of shares in compensation schemes for employees and other share awards.
Co-founder Evan Williams is the biggest shareholder in the firm with a stake of more than 10% worth more than a billion dollars.
Another of the founders, Jack Dorsey, will also become a very rich man. His 4% stake is worth more than half a billion dollars.
Biz Stone, another co-founder, is thought to have made millions by selling holdings over the last few years.
But Noah Glass, also one of the originals, is believed to have made very little from the company’s success.
Twitter is selling 70 million shares, which will raise $1.82 billion, for the company.
Unlike Facebook, Twitter has chosen to trade its shares on the New York Stock Exchange.
Facebook’s debut on the Nasdaq – traditionally the market of choice for technology firms – was marred by delays and problems with orders.
The NYSE has already tested trading of Twitter’s shares to try to avoid any technical hitches.
Twitter shares will trade under the symbol “TWTR”.
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