Yudhoyono, due to take office next week after a landslide election victory over incumbent Megawati Sukarnopturi, said he would start interviewing candidates on Friday and would ask them to sign an "accountability contract".
The new defense minister would be a person who understands "the place of the military in national life, democracy and human rights", the former general told reporters at his house in Bogor, south of Jakarta.
"For that position I have chosen to place a civilian who understands defense issues so that military reform can proceed well and defense policies can be developed in a good manner," he said.
Under former dictator Suharto the military was allowed to grow into a potent political force, controlling various civilian positions and enjoying reserved seats in parliament.
Since Suharto's downfall in 1998 the armed forces have been under strong pressure to abandon politics and atone for human rights abuses. Their right to legislative seats was abolished this year.
The United States has tied any resumption of military cooperation with Indonesia to military reform, including the calling to account of army-backed militia violence surrounding East Timor's independence vote in 1999.
Military cooperation with the United States was sharply reduced in 1999 by a Congressional amendment during the East Timor turmoil in which 1,400 people died, according to the United Nations.
Yudhoyono, who is expected to announce his cabinet on the day of his October 20 inauguration, said Thursday the body will consist of 34 members to be chosen for their "personal integrity, capability, experience and acceptability".
The president-elect said he would revive ministries of sports and housing scrapped following Suharto's resignation, and intended to split the trade and industry portfolio.
Yudhoyono, who will be Indonesia's first democratically elected leader, has made ambitious pledges to reform the country's sluggish economy and stamp out endemic corruption which has scared away badly needed foreign investment.