The Medibank Private share market offer has beaten expectations, raising almost $5.7 billion.
Finance Minister Mathias Cormann said there was very strong demand from both retail and institutional investors.
The final price for retail investors was $2 per share, a 7 per cent discount on the $2.15 per share price institutional investors paid.
Retail investors were allocated the majority of shares on issue.
Senator Cormann said the split was in line with previous privatisations.
"We felt it was appropriate to allocate 60 per cent to mums and dads across Australia to ensure that they can appropriately share in the future of Medibank," he told reporters on Sunday.
Senator Cormann didn't comment specifically on some fund manager observations that Australia's largest private health insurance company wasn't a big growth prospect but rather on the issue of cost-cutting, and the push for a leaner operational structure.
The privatisation was a win for its 3.8 million policy holders, Senator Cormann said, because it would provide better services.
"And it's obviously a win for Australian taxpayers because they have been able to release the capital that was tied up in Medibank," he said.
"We are in a position now to be able to release that capital in job-creating, productivity-enhancing infrastructure.
"The truth is Medibank Private is a good business, a very well known brand ... so there's lots of opportunity," he said.
Senator Cormann added the federal government had always believed Medibank Private would perform better in private hands than in public ownership.
"They will be more flexible in pursuing growth opportunities," he said.
"They will have better access to capital markets and will have the opportunity to perform and do the best they can without the restrictions of government ownership."
Senator Cormann said scoping studies for potential privatisations including Australian Hearing, Defence Housing Australia, the Royal Australian Mint and Registry Services at the Australian Securities and Investments Commission had not not yet been completed.
Medibank Private lists on the Australian Securities Exchange on Tuesday.
