Between January and March this year, 17,828 properties changed hands, a 22.9% rise on the same period in 2013.
It is the highest number recorded for the quarter since 2007/08, according to Registers of Scotland.
The total value of sales across Scotland registered in the quarter increased by 27.2% compared to the previous year to more than £2.73 billion.
Kenny Crawford, Registers of Scotland's director of commercial services, said: "This is the third successive quarter that volumes have been up over 22% on the previous year, illustrating consolidated growth in the Scottish property market.
"This is a picture that we're seeing across Scotland, with all local authorities showing an increase in the volume of sales for this quarter compared to the previous year.
"Prices are also up by an average of 3.5%, although this is more of a mixed picture across the country, with an increase of 24.9% in Inverclyde and a fall of 14.3% in Midlothian."
Inverclyde saw the biggest rise in prices, with an average price of £128,340, up 24.9% on the same quarter last year.
The highest house prices were in East Dunbartonshire, where a property costs £219,731, up 4.6% on that period in 2013.
Prices were lowest in East Ayrshire, where an average property cost £100,024, down 3.9% on last year.
The largest percentage price fall was in Midlothian, where they dropped 14.3% to an average of £157,690.
Housing minister Margaret Burgess said: "I welcome the Registers of Scotland figures, which show a 22.9% increase in the numbers of homes sold between January and March this year, compared with the same period last year.
"This is the third successive quarter that volumes are up over 22% on the previous year, illustrating consolidated growth in the volume of sales.
"The Scottish Government is taking action to stimulate the housing market and through our Help to Buy (Scotland) scheme we are providing £235 million to help more people, including first and second-time buyers, to purchase new-build houses."
Edinburgh remains the largest market with sales of just under £430 million for the quarter, up 28.4% on the same quarter last year.
Angus showed the highest percentage rise, with the value of sales increasing by 59.2%.
Registers of Scotland said that prices increased for all property types in this quarter, with terraced properties seeing the biggest rise at 2.6%.