Riigikogu members elected Isamaa chairman Helir-Valdor Seeder and EKRE chairman Martin Helme as board members on Tuesday.
Seeder received 46 votes and Helme 35.
Eighty-four MPs cast their votes and three ballots were deemed invalid.
The board consists of one president and two vice-presidents. Its role is to coordinate the work of the parliament and members are elected for one year.
The president of the Riigikogu, currently Jüri Ratas (Center), is the second most important official in the country after the President of Estonia, and can temporarily carry out their duties if need be.
Due to seveal MPs returning to the parliament and others becoming ministers, several changes have been made to the composition of the 101-seat Riigikogu.
Reform MPs Aivar Viidik, Ülle Rajasalu and Tiiu Aro will leave the Riigikogu to make room for former ministers Andres Sutt, Maris Lauri and Liina Kersna.
SDE's Toomas Jürgenstein and Reili Rand will join the parliament in place of Riina Sikkut and Lauri Läänemets, who will take up ministerial positions.
Siim Kiisler, who was expelled from Isamaa in March for being a member of the Parempoolsed faction, will replace Urmas Reinsalu, who has become foreign minister.
Editor: Helen Wright