Writing in the Sunday Herald, the Finance Secretary says a combination of rising oil prices and a wave of recent investments in Scottish fields mean both production and revenues from the North Sea will surge from 2016.
Putting the 40-year-old debate over "Scotland's Oil" back at the heart of the independence campaign, the SNP Government will publish its own detailed projections on the subject this week.
The forecasts are expected to be far rosier than those from the UK Office for Budget Responsibility (OBR), which twice downgraded North Sea oil revenue projections last year.
The OBR oil figures suggest Scotland's deficit as a percentage of its GDP would be larger than that of the UK's by 2016-17, reversing a recent trend which has seen Scotland relatively better off than the UK since 2008.
Government Expenditure and Revenue Scotland (Gers) figures published last week suggested that Scotland would be £4.4 billion, or £824 per person, relatively better off than the rest of the UK in 2011-12.
Swinney said that would make Scotland the eighth-wealthiest country in the Organisation for Economic Co-operation and Development (OECD), compared with the UK's 17th place.
The Government has produced a table comparing the OECD countries' GDP per head in 2011, including a Scottish figure based on last week's Gers statistics.
Swinney's projections come in the wake of a leaked Cabinet paper in which he admitted 12 months ago that the "high degree of uncertainty" around oil prices would make financial planning harder after independence, with oil revenues accounting for as much as 13% of Scottish tax receipts.
The leaked paper also accepted OBR forecasts from March 2012 predicting declining oil revenues in the near future, and warned the rising costs of looking after Scotland's ageing population implied tough spending choices ahead.
It was seized on by the unionist parties to claim that, while the SNP was brutally honest about the country's finances in private, the party painted a deceptively upbeat picture in public.
But Swinney is now questioning the OBR projections. He points out the OBR assumption that oil will be $92 a barrel in 2017 is considerably lower than the $130 estimated by Westminster's own Department of Energy and Climate Change, or the $150 per barrel forecast by the OECD.
In addition, Swinney says that recent investment by the North Sea oil industry is expected to yield an extra £3bn of revenues in 2017 when the new developments come on stream.
Today, the Finance Secretary writes: "Taken together, this surge in the investment and the rising price of oil mean that the early years of an independent Scotland are timed to coincide with a massive North Sea oil boom.
"The question every voter in Scotland must ask themselves between now and the autumn of next year is whether, given all these facts, Scotland can afford not to be independent."
Labour finance spokesman Ken Macintosh said Swinney's convenient oil boom figures should be treated with "extreme scepticism".
He said: "Whatever they [the SNP] claim is going to be very short-term, but independence is forever. What we all know for sure is that the oil is declining and that the reserves are becoming more difficult to get out and maintenance is costlier. So new investment is no guarantee of increased revenue."
Scottish Conservative leader Ruth Davidson said: "Alex Salmond is arrogant to think that if he now comes up with his own figures, simply to suit the SNP's political agenda, they will carry more weight with the industry.
"The public will not be fooled by his latest attempt at manipulating the figures to suit his own ends."
Michael Moore, the LibDem Scottish Secretary, called for "clear and accurate" figures in the independence debate: "We need a clear and accurate understanding about the choices an independent Scotland would face, not a debate obscured by bluster and diversion."