Interior Minister Yassin Elmi Bouh told the BBC the pilots were handed over last week after agreeing to go home.
A third man, their flight engineer, did not want to return and is still in Djibouti, he said.
The United Nations refugee agency (UNHCR) has expressed fears the deported pilots could face treason charges which carry the death sentence.
Djibouti is a signatory to the United Nations Convention on refugees, which prohibits expulsion or return of a refugee to a country where his or her life or freedom may be threatened.
Family members of the pilots in Ethiopia’s capital Addis Ababa rejected the allegations of the Djiboutian minister saying that the two never intended to come back to Ethiopia.
Eight Ethiopian airmen asked for asylum in Belarus last month.
At least 36 people were killed in Ethiopia after security forces fired at people protesting at alleged electoral fraud last month.
Mr Bouh told me the flight engineer, who is believed to have sought asylum with the two Ethiopian Air Force pilots on 9 June, could stay in Djibouti as long as he wishes.
He added that although Djibouti and Ethiopia share cordial relations, his country does not want to trample on international conventions on human rights in order to keep these relations.
Family members say the pilots are being held in an air force base outside Addis Ababa and are not allowed visitors.
"They would have been with us and not lurking in jail if they were brought back voluntarily," a tearful Senait Teferra, sister to one of the pilots, told me.
The relatives say that they have been visiting international organisations like the Red Cross and the UNHCR in a bid to secure the pilots’ release.
UN officials have confirmed that they failed to gain access to the airmen in Djibouti to determine whether they deserve refugee status.
"Despite earlier indications from government officials that we would be able to meet the Ethiopians, we still have not seen them and are growing increasingly concerned that the pilots may have been returned to Ethiopia against their will," UNHCR spokesman Ron Redmond told reporters in Geneva on Friday.
Kamel Morjane, UN assistant high commissioner for refugees, also wrote to Djibouti’s Foreign Minister Mahamoud Ali Youssouf last week expressing concern on the airmen’s fate.
"It is essential for the UNHCR and Djibouti authorities to find an appropriate solution in conformity with international refugee law," part of the letter read.
Officials at the Ethiopia’s Foreign Affairs Ministry declined to comment on the matter despite the numerous calls I made to them.
"They would have been with us and not lurking in jail if they were brought back voluntarily"
Sister of a pilot