Sir Harry Burns, who stepped down as chief medical officer for Scotland earlier this year, also told how he feared for the NHS in England, where ministers have made "very different" decisions to Scotland.
Those campaigning for independence welcomed Sir Harry's comments, which come less than two months before voters in Scotland decide the country's future in a referendum.
Sir Harry said: "The question is, would people in an independent country feel more in control of their lives?
"If they did, then that would be very positive for their health. If people felt that they were able to engage more with local government, with central government and make choices more easily for themselves then that would improve their health."
But he added the question of how leaving the UK and becoming independent would make people feel more in control would "depend very much on the political decisions that are made".
He stated: "At the moment, decisions - particularly about the health service - being made in England are very different from the decisions being made in Scotland.
"That is very important because I fear for the way the health service is going in England."
SNP MSP Aileen McLeod, a member of Holyrood's Health Committee, said the comments from the "highly respected former chief medical officer are very welcome indeed".
She added: "Sir Harry recognises the opportunities independence could bring for Scotland's health as a nation, stating that if this led to people feeling more in control of their lives then their health would improve.
"Sir Harry also adds to the growing number of people raising concern about the NHS south of the border. Dr Philippa Whitford - a top consultant breast cancer surgeon - recently spoke out about NHS privatisation, warning that there would not be a health service south of the border in five years' time.
"With the powers of the Scottish Parliament we have been able to protect our NHS from privatisation. But Westminster remains obsessed with dismantling the NHS - and cuts to its budget south of the border would have a knock-on impact in Scotland in the event of a No vote. This is a risk we can't take.
"Only a Yes vote gives us the powers we need to ensure that Westminster privatisation of the NHS stops at the border - and that the NHS in Scotland can continue to deliver world-class health care for everyone who needs it."
Dr Willie Wilson, co-founder of the NHS for Yes group, said: "When someone of Sir Harry's stature and expertise says that independence could have a very positive impact on improving the country's health, everybody should take notice."
He added: "'What Sir Harry says is both timely and sensible. We are fortunate in Scotland that the NHS is devolved but devolution cannot give the health service the protection it needs when Westminster continues to hold the purse strings.
"Unless we seize the opportunity that a Yes vote offers, it is very likely that Scotland, against our will, could be forced down the route of privatisation and commercialisation of our public health service, as is happening right now in England and Wales."
A Scottish Labour spokesman said: "Whether Scotland votes Yes or No, we will still face significant challenges in delivering the kind of NHS people want with an ageing population and squeezed budgets.
"Scotland's top doctor has described the SNP's running of the NHS as a car crash, and until this government stop seeing everything through the prism of independence, patients will continue to pay the price."