Gross Domestic Product (GDP) increased slightly by 0.6% during the third quarter of last year, and by 0.4% compared with the same time in 2011.
Finance Secretary John Swinney said: "These figures show that the Scottish economy has returned to growth after two quarters of contraction.
"Scotland's improved economic performance compares well to that of the UK where growth was supported by the temporary impact of the Olympics.
"However, there is no room for complacency. Recovery remains fragile - demonstrated by last week's flash estimate of a contraction in UK output during Q4 2012 - and the UK Government's continuing inaction risks a return to recession for the third time since the financial crisis of 2008."
Despite the overall growth, the construction sector output fell 0.4% in the third quarter and by 7.1% compared with the same time the previous year.
The services sector, which covers areas such as hotels and transport, grew 0.3% in the third quarter. Services account for about 72% of the Scottish economy.
At the same time there was 1.9% growth in the production sector.
Mr Swinney said budget negotiations at Holyrood are focused on construction, skills, employment and a "green economic stimulus".
He said: "Through immediate infrastructure investment we are providing a boost to Scotland's construction sector and wider economy and we are also maintaining the most supportive business environment in the UK.
"With the full fiscal and economic powers of independence the Scottish Government could do even more to strengthen our economy and create jobs."
Liz Cameron, chief executive of Scottish Chambers of Commerce, said the underlying performance of the economy "remains pretty much flat".
She said: "The good news is that there is capacity for growth in our economy and that businesses across the country are well placed to take advantage of the new opportunities that will arise from an upturn in demand.
"Average household disposable income grew marginally in Scotland last year and there remains significant opportunity available to businesses in terms of overseas sales. Coupled with the right level of support from government, we are confident that meaningful growth can return to our economy, but 2013 will be a challenging year."
Tourism is one area of great potential, she said.
Labour finance spokesman Ken Macintosh said Scotland is trapped between two governments making wrong decisions.
"It is very worrying that the construction sector contracted again during this period and that unemployment in the building industry is up on the previous month," he said.
"There is so much more the Scottish Government could be doing to replace the almost 40,000 jobs the sector has lost in this area alone under the SNP.
"Given that housing makes up almost 40% of the Scottish construction sector, and every pound spent on housing generates almost £3 in the wider economy, the Scottish Government should be increasing spending on housing as a good way to stimulate the economy not cutting it.
"That is why Scottish Labour are calling on John Swinney to spend the extra UK money on housing investment to provide a much needed boost to Scotland's hard-hit construction sector and help solve Scotland's housing crisis."
Conservative finance spokesman Gavin Brown said: "The boost in economic growth is welcome, but we have to remember this was only for the months of July until September.
"Fourth quarter figures for the UK showed a fall, so we have to be cautious about whether today's figures are a true indication that Scotland's economy is fully back to recovery."
Liberal Democrat leader Willie Rennie welcomed the new figures but said: "The message to the Scottish Government is that it cannot afford to dither any further on getting capital investment projects up and running.
"They fell short by £300 million this year with their Futures Trust and have declined to start identifying projects in 2014 to use the extra capital resources provided by the UK Government."
Scottish Secretary Michael Moore said: "Today's positive GDP figures are good news and very encouraging for Scotland's families and firms.
"We all want to see Scotland's economy growing and creating jobs and Scotland's two governments have to continue working together to make that happen.
"The economies of Scotland and the rest of the UK are connected in a beneficial way. The latest figures showing two-thirds of Scotland's exports, worth £45.5 billion, go to the rest of the UK show the strength of our single market very clearly."