The area also recorded the third highest average cost of a home in Scotland, at £226,510, and the number of properties sold is also up - by 13 per cent.
It is the ninth month in a row prices have risen, according to the latest LSL Scotland House Price Index.
According to the report, overall in Scotland the average house price is 4.3 per cent up on last year.
A spokesman for estate agents Savills said: “East Dunbartonshire is one of the leaders in the current market.
“To me, the volume of sales is the important factor, and sales are 13 per cent higher than last year.
“Demand is outstripping supply and this is pushing up prices.”
He added: “Locations like Bearsden, Milngavie and Lenzie are all very desirable places to live with good schools and good transport links.
“I would expect growth to continue in the area as a result.”