The strong debut for the social networking site's initial public offering exceeded even Wall Street's expectations.
The closing price gives Twitter a value of more than $31bn (£19.3bn).
Although the closing price fell 20 cents short of the opening price of $45.10, it was still 73% above the $26 IPO price.
Traders and journalists eager to see how the company would fair in its much-anticipated debut packed the NYSE floor.
Twitter co-founder Jack Dorsey told Sky News he was feeling "excellent" as he walked to a viewing platform to observe the start of trading.
The company's shares leapt to more than $45.70 within three hours - a sign hat investors were willing to bet on the company's potential growth.
The priced climbed to as high as $50.09 on the day.
The strong debut came despite the fact that Twitter has never turned a profit in seven years of existence.
Revenue has been growing, but the company is also investing heavily in more data centres and hiring more employees.
Some of Twitter's users, including Star Trek actor Sir Patrick Stewart, were given the opportunity to ring the opening bell instead of executives.
The company also sent a tweet to mark the occasion, posting a one-word message which read: "#Ring!"
Twitter initially offered 70 million shares, with an option to buy another 10.5 million.
The company boasts 230 million global users, including heads of state and celebrities.
However, the company lost $65m (£40m) in its most recent quarter and questions remain about its long-term prospects.
Twitter had initially set a price range of $17 (£10.57) to $20 (£12.44) but raised the range on Monday after an enthusiastic response from prospective investors.
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