"The president has asked me to form a government and I accepted and thanked him for the honour," the 73 year-old veteran of Turkish politics told journalists.
Outgoing Prime Minister Mesut Yilmaz's minority government lost a vote of confidence last week over allegations of corruption.
Mr Yilmaz was accused of entertaining ties with the mafia and tampering with the $600m sale of a state bank. He has denied the charges and has already taken legal action to clear his name.
Correspondents say the new administration could be a three-way coalition involving Mr Ecevit's own Democratic Left Party together with Mr Yilmaz's Motherland Party and the True Path Party of former Prime Minister, Tansu Ciller.
The grouping would have a large majority in parliament.
Mr Ecevit served three spells as prime minister in the 1970s and was deputy prime minister in Mesut Yilmaz's cabinet.
On Monday, the armed forces issued a statement warning Turkey's politicians not to drag it into arguments over the formation of a new government.
The military sees itself as the guardian of Turkey's secular constitution, and is concerned that the country's secular politicians should work together to exclude the pro-Islamist Virtue Party.
Although the Virtue Party is the largest political group in parliament, the military is opposed to it leading the country.
Parliament has set elections for April next year. However, Mr Ecevit said that even though his government would not be in office for long, it should not be thought of as a lame duck administration.
He said it was important to maintain economic stability and to prevent any foreign countries taking advantage of Turkey's position, and referred to the continuing dispute with Italy about the fate of the Kurdish rebel leader, Abdullah Ocalan.
Turkey has called for Mr Ocalan to be extradited, but Italy has refused to send him back.
Country profiles
Turkish military warns politicians
(30 Nov 98 | Europe)
Talks start for new Turkish Government
(25 Nov 98 | Europe)
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