The explosions happened in the Bole district of Ethiopia's capital city, about 5 kilometres from the Addis Ababa Stadium where thousands of fans were gathering for the play-off match.
It is believed the bombers, of Somali origin, set off their devices early after panicking at the significant police presence throughout the city, with government spokesman Shimeles Kemal confirming their intended target was either the 35,000 capacity crowd in the ground or one of the areas where supporters were grouped to watch the game on big screens.
"They were Somali nationals and plotted to carry out a suicide attack disguised as fans on either the stadium or areas where large crowds gathered to watch the game," government spokesman Shimeles Kemal was quoted as saying by Reuters.
"Heavy police presence must have caused their nervousness and state of agitation which led to the detonation that caused their own deaths."
Explosives, football shirts, grenades and human remains were found at a residential address in the Bole district, close to the Saro-Maria hotel where the Nigerian team stayed while in the country. Three other suspects were detained by police.
The area is home to a number of Somali refugees.
Nigeria defeated their hosts 2-1 at the packed national stadium in the first leg of the play-off for Brazil 2014, with the return leg set to take place in Calabar on November 16.