TeliaSonera already which already owns 61 percent of the company.
"The Estonian government decided at its Thursday session to sell all the shares the state has in Eesti Telekom" for some four billion kroons ($378 million), cabinet spokesperson Liina Lepik told AFP.
At the end of August, Swedish-Finnish telecoms group TeliaSonera made a 5.1 billion kroon bid for the remainder of Eesti Telekom.
The remaining 12 percent of the company is held by private shareholders.
TeliaSonera - which holds assets across eastern Europe and Central Asia - first acquired a minority interest in Eesti Telekom in the early 1990s.
Lepik said the deal would boost Estonia's budget balance starting this year.
Estonia's centre-right minority government has said the sale is crucial amid a deep economic crisis, but the opposition has blasted it, saying Eesti Telekom provided the state with a stable source of income.
Estonia, which shifted rapidly from a communist command economy to the free market after independence from the Soviet bloc in 1991, had enjoyed a reputation as a "tiger" in the European Union, which it joined in 2004.
But the country of 1.3 million people swung into a sharp recession in 2008 and its economy is forecast to shrink by 15.3 percent this year.