Vimpelcom CEO Aleksandr Izosimov said the purchase would put his company "firmly on track to become the No. 1" telecommunications firm in the CIS.
Vimpelcom said it would also assume $456 million of Kyivstar's debt.
The Russian firm has already purchased URS, which was Ukraine's fourth-largest mobile operator.
The offer to buy Kyivstar may cause tension between Vimpelcom's main shareholders, Russia's Alfa Group and Norway's Telenor. Those two groups disagree on Vimpelcom's strategy in Ukraine.
RFE/RL Russia Report
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