The number of residential properties sold between April and June was up 22.4% on the same period in 2013.
A total of 24,351 properties changed hands - the highest recorded for the quarter since 2008/09 - while the average price of a property was £162,122.
It is the fourth successive quarter in which sales have increased above 22% compared with the same period the previous year.
Registers of Scotland's director of commercial services Kenny Crawford said: "It's also the first time in almost four years that we've seen the average house price rise by more than 5%, bringing the average residential property price to £162,122."
Renfrewshire recorded the highest percentage rise in average price compared with the same quarter of the previous year, up 16.8% to £128,138.
The largest percentage fall in price was in Midlothian, which dropped 6.3% to an average price of £169,014.
Edinburgh remains the highest value market with total sales of just under £670 million for the quarter, an increase of 39.4% compared with the same quarter last year.
Housing minister Margaret Burgess said: "This is the fourth successive quarter that volumes are up over 22 per cent on the previous year, illustrating sustained growth in the volume of sales.
"This shows that six years after the financial crash, the housing market in Scotland is showing real signs of recovery, which is great news for households wanting to buy their first home or move house, as well as for those working in the housing market."