Dzombic was the finance minister in the previous Dodik-led government.
Dodik was elected president of the Republic of Srpska at general elections held in Bosnia and Herzegovina on 3 October.
The appointment of the Dzombic cabinet was supported by the SNSD (Party of Independent Social Democrats) and another two minor Serb parties.
According to the entity's constitution, the Bosnian Serb government must include, apart from Serbs, five ministers of Bosnian Muslim (Bosniak) descent and three Croats.
Considering the Croat personnel, only Davor Cordas from the Croatian Democratic Union of Bosnia and Herzegovina (HDZ BiH), who will serve as minister for refugees, comes from a Croat party, while the other two ministerial posts intended for Croats, and ministerial posts intended for Bosniaks are filled by candidates from the ruling Serb parties.
The new premier said he would not allow any attempt to transfer powers from the entity to the state of Bosnia and Herzegovina and that he would also launch proceedings to question cases of earlier transfers of powers.
The cabinet led by Dzombic will formally step into office after the entity's upper house approves it. The legitimacy of the House of Nations in the Serb entity is being questioned by the Bosniak deputies' club, which holds the election of the house chairman to be disputable.