The acquisition will be completed on June 22, 2015, Elering told the stock exchange.
Following the acquisition Elering will hold 89.1 percent of the stock capital of AS Vorguteenus Valdus.
The CEO of Elering, Taavi Veskimagi, said the goal was to bring the size of the holding to 100 percent and the transaction bring Elering one step closer to that goal.
Previously Elering acquired the holding of Fortum in Vorguteenus Valdus at the beginning of this year and the holdings of small shareholders earlier this month. All the shares were obtained by Elering using the same pricing model.
Elering said its final goal is to become the sole owner of the transmission network and bring management of the electricity and gas networks together in one company.