The government’s remaining shares, roughly two thirds of its 51.8 percent stake in the telco, will be parked in the Future Fund.
The stocks will be sold in a public float this October and November, open to retail and institutional investors in Australia and overseas.
A year ago A$8 billion worth of Telstra stocks would have been about one-quarter of the government's 51.8 percent stake.
But Telstra's share price has plunged since the government got the sale laws through parliament, slicing the value of the government's stake from A$31 billion to about A$21 billion.
Prime Minister John Howard made the surprise announcement late on Friday, just hours after refusing to be drawn on the sale's timing.
His announcement appeared to take senior colleagues by surprise, with Deputy Prime Minister Mark Vaile telling reporters less than an hour earlier that no sale was imminent.
Mr Howard said the government would have sold its share of the telco for a much better price much earlier had the opposition Labor party not blocked legislation in the Senate.
"The government has also been committed to the full privatisation of Telstra," Mr Howard told reporters in Hobart.
"We would have sold the remaining shares in Telstra a lot earlier at a higher price ... had it not been for the legislation being blocked in the Senate by the Labor Party and by others."
Mr Howard said he had held discussions with Telstra chairman Don McGauchie over the past few days and had been assured that the company would cooperate to make the sale a success.
"Telstra's chairman, board and senior management have assured the government of their strong commitment to this sale and their ongoing cooperation," he said.
"In particular, Telstra has made it clear that they will not use the sale process as a vehicle to campaign for changes to the regulatory regime."
Mr Howard said the government had gone to the past four elections promising to sell its Telstra shares.
"For too long, the government has had a massive conflict of interest, as the owner and seller of Australia's largest telco; and as the industry regulator," he said.
"Selling Telstra continues to be good policy that is in the interests of existing Telstra shareholders, in the interests of the company and in the interests of the broader community."
Mr Howard said the government believed it could achieve an appropriate return for taxpayers, despite Telstra's plunging stocks.
"Our sale advisers have been closely assessing market conditions and their unanimous advice to the government is that there is sufficient demand to support an offer of this magnitude and it can be done at a fair price," he said.
Retail investors will be able to pay for their shares in two instalments over 18 months.
The sale proceeds will be invested in the Future Fund, helping to address the challenges posed by an ageing population.
Mr Howard said customers would not lose out in the sale.
"The government does not have to own Telstra in order to regulate it," he said.
"The government regulates the entire telecommunications industry, regardless of Telstra's ownership structure.
"The cornerstone safeguards of the Universal Service Obligation, the Customer Service Guarantee, price controls and other important consumer protections, will continue to apply to Telstra and all carriers because they are all provided in regulation and not subject to review until 2009."
A final decision to launch the offer remains subject to market conditions being conducive for a sale which achieves the government's sale objectives.