The sale was oversubscribed by more than 500%, a sign that investors have renewed appetite for Kenya's economy after violence in the country following elections earlier this year, analysts said.
The popularity of the stock offering meant most Kenyans received only 21% of the shares they applied for.
Michael Joseph, Safaricom's chief executive said: "We went out of our way to create as many shares as we possibly could to let people apply."
Unlike many Western countries, Kenya's mobile phone market is not saturated - only a third of Kenya's 36 million people own a mobile phone.
Analysts also said Safaricom's strategy of targeting low-income Kenyans would help boost its customer base.
President Mwai Kibaki, who launched Safaricom's trading debut said: "This IPO is the most attractive in our history."
But the share sale caused some controversy.
Opposition parties had tried to delay the issue because of uncertainty over Safaricom's other shareholders.
While the government insists it currently owns 60% of Safaricom with the other 40% in the hands of UK giant Vodafone, opposition groups say another firm called Mobitelea also has an interest.
Registered in Guernsey in the Channel Islands, Mobitelea's owners remain unknown.
Media reports in Kenya have speculated that Mobitelea owns as much as 10% of Safaricom.
Safaricom is East Africa's most profitable company, it made profits of $370m last year.
Bookmark with:
What are these?