The floatation on the Iraq Stock Exchange was seen as a test of investor confidence in the country.
It could reassure international investors, many of whom remain wary of the risky Iraqi market, influenced by continued sectarian violence and political deadlock.
In the latest violence Sunday, a suicide car bomber joined by other suicide attackers on foot assaulted a provincial police headquarters in the disputed northern Iraqi city of Kirkuk, killing at least 15 people and wounding 90 others, officials said.
Asiacell had offered a quarter of its shares, or 67.5 billion, as part of licensing requirements. The initial share price was set at 22 Iraqi dinars, or just under 2 cents.
With Asiacell's share offer, the market capitalization of the ISX nearly doubled to about $9 billion, up from $4.7 billion, said Taha al-Rubaye, head of the stock exchange.
Foreign investors bought about two-thirds of the stock, said Shwan Taha, whose brokerage firm, Rabee Securities, organized the sale.
Regular trading of Asiacell stock is set to begin Monday.
Al-Rubaye said it's the first stock float on the ISX, which was set up in 2004, a year after a U.S.-led invasion toppled Iraqi dictator Saddam Hussein. Al-Rubaye said he believes it's also the largest IPO in the Middle East in nearly five years.
The government-controlled oil sector dominates the Iraqi economy, dwarfing a small private sector and capital market. Al-Rubaye said he hopes the Asiacell offer is a sign of change.
Geoffrey Batt, a New York-based fund manager who has been investing on the Baghdad exchange since 2008, said that "Asiacell is demonstrable evidence that Iraq does in fact have a viable capital market."
"It indicates that this is a market capable of attracting significant investment from local and foreign sources," he said.
Asiacell is one of three major Iraqi telecom companies, along with Zain Iraq, part of Kuwait's Zain, and Korek, an affiliate of France Telecom. The Gulf state of Qatar's government-backed Qatar Telecom has a majority stake in Asiacell.
The three companies were required to list shares on the stock exchange as a condition of their 15-year operating licenses, which cost $1.25 billion when they were acquired in 2007.
All three missed a deadline in August 2011 to offer shares to the public.