In the previous three years, the volume of residential sales within five miles of the new stops has risen by 50.2% in Midlothian and 26.3% in the Scottish Borders.
The figures for the whole local authority areas of Midlothian and the Scottish Borders rose by 60.6% and 30.1% respectively.
Overall, figures in Scotland rose by 28.2%.
The average house price has remained largely unaffected.
Since the railway was announced in 2006, prices in the Midlothian catchment area have grown 6.1% to £166,639, while houses within five miles of the new Scottish Borders stations have seen average prices increase by 4.5% to £143,283.
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Across the region as a whole, average house prices in Midlothian have risen by 13.4% and by 9.5% in the Scottish Borders.
In Scotland, there has been a 16.1% rise in average house prices during the same period.
RoS' head of data, Rhona Mackay, said: "We have seen an increase in the volume of sales around the new Borders railway stations, but this is slightly lower than the volumes seen in the local authority areas as a whole. Prices are also up, but again this is lower in the five mile catchment areas than the wider local authority areas where the increase is more substantial.
"It is widely expected that the new line will stimulate interest in the property market in the areas close to the stations, and there have already been a number of new-build developments within the railway catchment areas in recent years, so it will be interesting to revisit these statistics again once the new link is up and running."
Services along the route are scheduled to begin on 6 September.
The full report is available to view here.
(LM)
