The average cost of a two-bedroom flat now stands at almost £900. The same type of property costs about £550 across the rest of Scotland, on average, excluding the capital.
Political leaders say rents are being "pushed sky high" because of a lack of affordable housing.
Private rents now account for about a third of all households in Edinburgh - roughly 140,000 city residents - as numbers soared in the years following the financial crash.
There has been a rise of 33.7% in rent costs between 2010 and 2017 in Edinburgh and the Lothians, the Scottish Government figures show, while rising 6.9% between 2016 and 2017. Glasgow has also seen a 32.1% since the start of the decade and 7% over the year.
All other areas of Scotland are below the national average of 19.9% and 4.4% respectively.
Tory housing spokesman Graham Simpson said: "Rents are being pushed sky high, particularly for young people unable to get on the housing ladder.
“The SNP has pledged to build at least 50,000 new affordable homes over this Parliament, however, if they continue at the current rate they will miss this target by two years."
The Tories want to see greater use of brownfield developments and the creation of more New Towns to address the issue.
The average cost of renting a two bedroom property in Edinburgh and the Lothians jumped by more than £50 inside a year from £831 in 2016 to about £888 last year. At the top end of the property market, rents have reached £975 for a two-bedroom flat in the capital. The statistics are based on advertised rents for new lets and don't include changes in rents for existing tenants.
For a one-bedroom flat, it now costs more than £700 (£704) to rent a one-bedroom flat in the capital on average - up from £520 at the start of the year.
Adam Lang of Shelter Scotland, said: “Rent increases of these amounts will hurt those who are already living on a knife-edge.
“We already know that a great many families are struggling day-to-day to keep a roof over their heads. Affordability was the single biggest reason people came to Shelter Scotland with last year and private renters are the biggest group who contact Shelter Scotland for help.
Ministers have already introduced new private residential tenancies which will include a limit on one rent increase in a year, three months-notice of any increase and an opportunity to appeal to the housing and property chamber to have rent set by an independent party.