The statistics show the average house price from January to March was £173,830.
The figure is the highest recorded for any quarter since RoS began compiling statistics in 2003.
The highest rise was in East Lothian (28.6%) to an average of £248,902.
The total volume of sales across Scotland was 16,946, a decrease of 4.7% on the same quarter in the previous year.
Is it the second consecutive quarter that has seen sales volumes decrease and is the highest annual decrease in sales volumes since quarter one of 2011-2012.
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RoS' head of data, Hugh Welsh, said: "We've seen sustained growth in house prices throughout the 2014-15 financial year, with January to March's figures representing the highest quarterly increase in average price since quarter one of 2007-08.
"Future sales statistics will determine whether this is a one-off spike in quarter four average prices, or whether this is a trend that will continue."
West Dunbartonshire showed the largest percentage rise in the number of sales, with an increase of 10.6%.
The biggest percentage decrease was in Midlothian, which dropped 28.1% to 233 residential house sales.
The total value of sales across Scotland increased by 8% to just under £2.95 billion compared to the previous year.
The City of Edinburgh recorded the highest average for the quarter at £260,647, a 21.4% rise, along with the highest volume of sales at 2,123.
All property types showed an increase in average house price, with semi-detached properties recording the largest increase at 15%.
Apart from detached properties which increased in sales volumes to 9.1%, all other property types volumes decreased.
(LM)
