Lance Corporal John Gabriel and Lance Corporal Adamu Gideon, both of the Recce battalion in Nguru, Yobe state, are the soldiers. Their registration numbers are N/A13/69/1522 and N/A13/70/6552, respectively.
According to police spokesperson Dungus Abdulkarim, the suspects will face legal charges.
Lance Corporal Gabriel, the main suspect, admitted to the act and gave a detailed account of how he killed the clergyman and took his car.
A board of inquiry has been formed to determine the facts behind the regrettable tragedy, according to earlier statements from the army.
According to a statement signed by army spokesperson Kennedy Anyanwu, any soldier found wanting will face the wrath of the law.
“This incident is highly regrettable given the Sectors disposition and zero tolerance on violation of Code of Conduct and Rules of engagement for troops,” Anyanwu said,
Newsmen had reported the killing of Sheikh Goni Aisami-Gashua on Saturday.
The cleric was said to be travelling from Gashua to Kano when he was followed in a bus by the attackers.
Some Gashua residents told newsmen that the incident happened around 10am at Jajimaji, a distance of less than 30 kilometers away from Gashua, the hometown of the Senate President, Ahmad Lawan.
Police spokesman in the state, DSP Dungus Abdulkarim, in a telephone conversation with our correspondent said suspects wielding AK-47 rifles had been arrested and were in police custody.
Gashua has been one of the most peaceful communities in the state, even at the peak of the Boko Haram insurgency.