Letting firms say the return of demand, especially in prime areas, together with a slump in supply, will see average prices surging.
They say there is now a shortage of many of the city’s most popular types of property to rent, such as flats in the New Town, Marchmont and Bruntsfield.
High-flying executives moving into the city are said to have helped the recovery at the top end.
While the growth in the number of "reluctant landlords" putting their property up for rent because they could not sell had resulted in a tenants' market, agents say that is now changing.
DJ Alexander, one of Scotland's biggest independent letting agents, said the number of properties on its books had almost halved to just 130 in a few weeks. It let out 162 properties in May, just five short of its all-time record month. Coinciding with a shortage of new properties becoming available, the firm said that was set to lead to rising rent rates.
It said that one townhouse on its books in the New Town struggled to achieve the £1,700 it was advertised at nine months ago. But it has now been brought back on to the market at £2,500 a month, which it is confident of achieving.
In the "middle market" areas, it said that average two-bed flats now cost around £700 a month, compared with an average of about £650 a few months ago.
Rob Trotter, senior property manager at DJ Alexander, said: "The supply of new properties has slowed down so much, so rents are strengthening and landlords are starting to find it a lot easier to get people in.
"It is a huge turnaround on three or four months ago when there was so much on the market because all these unsold properties were getting dumped on the market."
He said that not many properties above £1,500 a month would be snapped up only a few months ago, but now new people were entering the markets with budgets of more than £2,000.
Some families are said to have been forced to sell their homes and rent in the short term before looking to buy.
The appearance of people looking to rent high-value property has been helped by boardroom reshuffles at firms such as Royal Bank of Scotland.
"The big employers haven't been employing as many lower level staff, which has certainly affected us," he said. "But they are taking on really senior people. It is the real big shots – such as senior executives – that are coming into town and looking to rent."
Edinburgh-based estate and letting agent Murray & Currie has launched a new marketing campaign to encourage people to rent out property because it has seen a sudden slump in supply across the city.