A spokesman for the government said General Gvero had made the decision to surrender voluntarily after meeting with the Serbian Justice Minister Zoran Stojkovic on Monday.
The charges against Gvero have not been made public but the Serbian government said Belgrade had received an indictment against the general from the International Criminal Tribunal for the former Yugoslavia, which is based at The Hague.
Gvero served in the Bosnian Serb army during Bosnia's 1992-95 inter-ethnic war. He was a deputy to wartime Serb army chief Ratko Mladic, one of the most wanted war-crimes fugitives still at large in the Balkans.
"General Gvero said that with this decision to surrender he wanted to fulfil his obligations to the state, his people and his family," the Serbian government said.
"The government of Serbia highly respects the decision, which is moral and in the interests of the state."
It said he would surrender on Thursday in the company of an official from Belgrade.
Serbia has come under mounting international pressure to arrest war-crimes fugitives, particularly Mladic who is wanted for the 1995 massacre of some 8000 Muslims at the eastern Bosnian town of Srebrenica.
Belgrade denies any knowledge of Mladic's whereabouts but chief UN war crimes prosecutor Carla Del Ponte has repeatedly claimed he is hiding in Serbia with the help of the Serbian military.