Barclays, which is one of the biggest market-makers and specialist firms on the NYSE trading floor, also handled Twitter's IPO last year.
Separately, Goldman Sachs will serve as "stabilization agent" to manage the deal's early floor trading, Dow Jones reported Wednesday.
Analysts believe demand for shares will be so strong that Alibaba could surpass the $16 billion raised by Facebook Inc. in 2012. That would value Alibaba at $150 billion to $200 billion, making it one of the most valuable U.S.-traded companies.
The shares will trade on the New York Stock Exchange under the ticker symbol BABA.
-By CNBC.com. The Associated Press contributed to this report.