Prices north of the border are now 5.5 per cent above the pre-economic downturn peak of June 2008, the Office for National Statistics (ONS) House Price Index shows.
The average price of a property in Scotland had risen to £207,000 by March this year.
The 14.6 per cent rise in the year to the end of March 2015 was up on 5.3 per cent to the end of February this year.
The report suggests the new land and buildings transaction tax (LBTT), which came into force on April 1 replacing stamp duty, may have had an impact on price increases.
On properties costing more than £254,000, tax rates are considerably higher under the LBTT rules than under the old stamp duty rates.
The ONS report said: “The number of mortgages for house sales in Scotland increased by approximately 50per cent between February and March 2015.
“A significant proportion of this increase in sales was for houses costing more than £500,000.
“These factors, along with a relatively small annual increase in Scotland prices of 0.8 per cent in March 2014, have led to the price index for Scotland increasing by 14.6 per cent when compared to a year earlier.
“It should also be noted that the land and buildings transaction tax replaced UK stamp duty land tax in Scotland from 1 April 2015, which may have had an impact on the increase in prices.”
Across the UK, house prices increased by 9.6 per cent in the year to March 2015, up from 7.4 per cent in the year to February 2015.
However housing and homelessness charity Shelter Scotland said more needs to done to tackle the country’s housing crisis.
Adam Lang, head of communications and policy at Shelter Scotland, said: “News from the Office for National Statistics that house prices in Scotland have seen their highest annual increase since 2007 is no reason for celebration. And at a time when many are struggling to afford a home and make ends meet, it’s ironic that some will see this is a positive sign the housing market is recovering.
“True recovery suggests a return to health. But, when wages are stagnant and housing costs are already high, an increase in house prices only makes it even harder for people - especially young families - to get a home of their own. For many people across Scotland these statistics are bad news.
“A healthy housing market is one where everyone has a secure, affordable home whether renting or buying, but many are being denied that right because Scotland has a housing crisis driven by a major shortage of affordable housing.
“To meaningfully tackle our housing crisis, we need to build 10,000 new social homes every year to help those for whom the prospect of a home of their own is still well out of reach.
“This will bring hope to the 150,500 households on council waiting lists and much-needed jobs to our construction industry.”