Tenants across Scotland are now paying £699 every month for their rent following an average 3.6% increase, according to research by lettings website Citylets.
But Aberdeen recorded a 10.9 per cent increase which pushed prices up to £1,066.
The results prompted concern about the scale of housing supply in some parts of the country.
The findings show the Edinburgh and Aberdeen markets are out-performing the national average, with the cost of renting a one-bedroom property in Aberdeen at about £673.
Rents in the capital average £848 per month, compared with £595 in Dundee and £628 in Glasgow.
In its quarterly report, Citylets also revealed rents for larger four-bedroom properties rose in all of the major cities over the past year.
Report authors said there is usually an increase around Easter in the number of larger properties coming on to the market to meet the high demand from students sorting their accommodation for the following year.
Thomas Ashdown, managing director of Citylets, said: “I wouldn’t say the market is facing any wholesale crisis at this time but it is clear that there are some areas where supply could be considered a concern.
“For the first time in a while we are seeing average rents in Edinburgh begin to climb on a trajectory that Aberdeen started to take two years ago.
“Scotland needs more homes in general and this appears to be increasingly true for property in the parts of the private rented sector.”
In Edinburgh average rents for one and two-bed properties are up 5.7% and 4.4% respectively and up 11.4 per cent and 10.7 per cent respectively in Aberdeen.