Rettie & Co said they have completed the 24th transaction of a property worth £1m or more in Edinburgh.
Sales of £1m-plus homes dropped back considerably after 2007, but the number of luxury properties changing hands has stabilised in recent years.
Edinburgh usually accounts for more than 40% of all such sales in Scotland, but sales are growing fastest in and around Aberdeen.
The majority of buyers of £1m houses are already located in Scotland, but there has been interest from overseas among buyers with strong Scottish connections.
Four £1m-plus houses sold in Glasgow this year, compared to none in 2012.
In Scotland, Rettie & Co had £20m of property for sale which had had offers accepted in the first two weeks of October, up 162% on the same period last year.
The firm's managing director Simon Rettie said: "The £1m-plus housing market has struggled alongside other parts of the housing sales market in recent years. However, there has been a notable improvement in market sentiment and confidence in 2013 and this is reflected in our sales of such properties this year.
"Typically, only around one in 10 sales of houses over £1m in Scotland go to an overseas buyer in any given year. Although far from a negligible market, the influence of overseas buyers on this particular housing market has been exaggerated by some."