Souter Investments, which has a 30% stake in the consortium that also includes Turkish firms Tepe, Akfen and Sera.
Tepe and Akfen own rights to operate Istanbul’s Ataturk airport, the largest in Turkey.
The amount of money paid by Souter Investments was not disclosed but transport industry sources said it could be as much as £155m. A spokesman for Mr Souter said he would not comment on the deal at this time.
In early March, Mr Souter decided to withdraw from the bidding for the Gourock-to-Dunoon ferry route to concentrate on the eastern European transport market.
The consortium saw off competition from four other bidders including a partnership of Turkey’s largest conglomerate, Koc Holding, and international ferry operator Stena, Global Yatirim’s Global Liman unit, Turkey’s Yildirim and Torunlar.
The privatisation process of the ferry company started on January 6 and the bidding period ended on March 31.
The sale price values IDO at 8.6 times its 2010 earnings before tax, interest, depreciation and amortisation, said Erkan Kurt, corporate director of broker EFG Istanbul.
IDO, a subsidiary of the Istanbul city government, had sales of 347 million lira in 2010 (£140.9m) and hopes to generate at least 380 million lira (£154.37m) in the current year.
Turkish media had speculated recently that the ferry company, which operates fast ferry lines around Istanbul, a city of more than 13 million people, and the Sea of Marmara, would be sold for $700m to $1bn.
Istanbul, Turkey’s largest city, is still growing, and sea transport is highly favoured, given heavy road congestion.
Mr Souter also runs Fullers Ferries, the leading ferry company in Auckland, New Zealand. Fullers operates 15 ferries and 16 buses, carrying 12.5 million passengers a year, according to the company.
The consortium will finance three-quarters of the purchase of IDO with loans, Irfan Erciyas, a board member of Akfen, told Turkish media after the auction. The transaction, which is subject to Turkish regulator approval, may be completed in three to four months, he added.
IDO, or Istanbul Deniz Otobusleri, transported 100 million passengers and seven million vehicles in 2010, according to the Turkish newspaper Hurriyet.
The company operates 52 vessels on 19 lines.
The ruling AK Party government is privatising major highways and bridges, including the two bridges across Istanbul’s Bosphorus Strait linking the city’s European and Asian sides.
A third bridge is also planned, while a rail tunnel under the Bosphorus is under construction.
The fast-growing country, which is seeking entry to the European Union, is eager to attract foreign cash for infrastructure development.
Souter Investments, based in Edinburgh, has a portfolio of 120 investments with a value of more than £400m, according to its website.
It has stakes in listed companies such as Stagecoach, the Perth-based rail and bus group. It also has holdings in unlisted firms including Fuller Ferries, Sunseeker Yachts, insurer Esure, and Falkirk-based bus maker Alexander Dennis, according to its 2010 Investment Review.