Some 25,579 residential properties changed hands in October to December last year.
It was the highest figure for this period since 2007/08 and up 26% on the same time in 2012.
The official statistics, published by Registers of Scotland, showed the average price of property for the last quarter of 2013 was £159,670.
A regional breakdown shows that East Renfrewshire was the most expensive place to buy in Scotland, with an average price of £222,906.
Edinburgh had the highest number of sales, with 2,951 properties changing hands, while 2,569 homes were sold in Glasgow.
East Lothian recorded the highest percentage rise in price, jumping almost 15% to £209,566, compared to the same period last year.
The largest percentage drop in average house prices was in Inverclyde, where values fell by 8.7% over the year to £116,085. But statisticians said it was an area accounting for little over 1% of the Scottish sales total, meaning it can be easily influenced by factors such as a large, high value sale or lots of sales at the lower end of the market.
Registers of Scotland commercial services director Kenny Crawford said there were price increases across all property types.
"The Scottish property market is definitely showing signs of improvement and renewed optimism, possibly partially fuelled by an influx of first-time buyers thanks to schemes such as Help to Buy," he said.
Housing Minister Margaret Burgess said: "We welcome the Registers of Scotland figures, which show a 26.1% increase in the numbers of homes sold between October and December this year, compared with the same period last year. This builds on the 22.5% increase in sales reported in the last quarter."
She went on: "The Scottish Government is taking action to stimulate the housing market, and through our Help to Buy scheme we are providing £220 million to help more people, including first and second-time buyers, to meet their home ownership aspirations.
"Over 100 house builders have registered with the scheme so far, and five lenders are offering mortgages under Help to Buy. So far over 1,200 people have applied and there have been 250 completed sales, demonstrating the popularity of the scheme.
"Help to Buy is also helping stimulate economic growth by supporting our housing industry - alongside our commitment to investing in affordable housing across Scotland."