On Friday, investor demand led the stock to make its debut at $92.70, more than 38% above its $68 initial price.
Alibaba's bankers then chose to buy additional shares, reports say.
That means the firm has surpassed the record $22.1bn China's Agricultural Bank raised in 2010.
At the end of trading on Friday, Alibaba had smashed several records - with trading volume in the first minutes beating that of Twitter's stock sale - but there was still some speculation about the overall size of the share sale.
Alibaba is now worth more $223bn - more than Facebook, Amazon and eBay.
As part of the terms of its stock offering, Alibaba's bankers were entitled to buy an additional 48 million shares, in addition to what had been offered to outside investors.
Most analysts indicated that if Alibaba's shares had fallen below the initial price, the bankers would probably choose not to purchase additional shares.
However, after Alibaba's shares debuted at $92.70 on Friday - significantly above their initial offering price of $68 - that turned out not to be the case.
In early US trading on Monday Alibaba's shares were down 4% at $90.04.
Chinese internet giant Alibaba has raised $25bn (Â£15bn) in its share flotation, according to US media, making it the largest initial public offering (IPO) in history.