Last November, VimpelCom acquired 90% of Armentel's stock from Hellenic Telecommunications Organization SA (OTE) for 341.9 million euros ($440 million).
A spokesmen for the Armenian government said the price quoted for the 10% stake accounts for one-ninth of the amount VimpelCom paid to the Greek company for the 90% stake in Armentel.
The Armenian government first proposed selling the remainder to VimpelCom last year, on condition that the company does not try to monopolize the post-Soviet South Caucasus nation's telecoms market.
Under the deal, VimpelCom will also take on Armentel's debt, totaling around 40 million euros ($51 million).
Armentel is Armenia's landline phone monopoly, which also offers Internet connection to providers and end-users. In addition, it is one of the two Armenian mobile phone operators, with about 400,000 subscribers across the country.
VimpelCom is Russia's second-largest mobile phone services provider, best known for its Beeline brand. It also operates in the former Soviet republics of Kazakhstan, Georgia, Tajikistan, Ukraine, and Uzbekistan.