Police say the man admitted he set the fire early Saturday at the Legend Oaks Apartment after getting into a fight with a tenant.
Officials were expected to file murder and arson charges on Monday.
The fire killed two-year-old Amiyah McClenton, and her babysitter, 34-year-old Brandi Johnson.
Residents say other tenants escaped after some residents ran through the hallways pounding on doors to alert people to the fire.
The American Red Cross helped 26 people who were displaced by the fire.