The company, which last month reported a 28.6 per cent rise in first-half profits to a record £23m, has handed Cubitt a brief directed from London, which includes the European capital markets.
Cubitt associate director Ilias Catsaros takes over the running of the account from GCI next month.
GCI has held the account since 2002 and is believed to have defended the business against one other agency.
It is understood that the new global brief could bring Cubitt as much as £250,000 a year in fees.
Tsakos has relocated the brief to London, because the City is home to most of the world's maritime underwriters. It is also within striking distance of the headquarters of other large shipping companies, many of whom are based in Europe.
The Greek company's recent surge in profits has been attributed to the sale of several older tankers and a new building contract swap. Gains on vessel sales contributed £14m to the first-half profit compared to £4.8m in the first half of 2004.
Tsakos is nearing its goal of 'a universally double-hull fleet', and will therefore shortly be seeking to offload the two remaining single-hull tankers out of a total of 26 tankers that it is currently operating.
So far this year, Tsakos has sold the single-sided, double-bottomed product carriers Pella and Dion for a gain of £4.9m, the single hull Aframax Panos G for £2.9m and sealed an Aframax new building contract for a profit of £6m.
The international tanker sector has profited in recent months because of a high demand for oil in the developing economies of India and China.
Demand for oil is expected to peak this month, as countries increase oil imports in anticipation of the winter months.