The 2013 Afcon champions will have the luxury to start the two-legged match campaign in Addis Ababa in October while the reverse fixture will hold in Nigeria in November.
The winners of the two-match play-off will automatically qualify for the Fifa World Cup coming up in Brazil next year.
Onigbinde said the only antidote for our qualification for the 2014 Fifa World Cup in Brazil is adequate preparations not the opponents as such.
"I've never bothered my head over whom I'm drawn against in any competition rather I pay undivided attention on preparations. So Nigerians shouldn't go dancing and drumming because they're drawn against Ethiopia rather commence immediate preparations.
"Football is a democrat, it's 11 players apiece at every point in time, I don't believe in the doctrine of minnows.
"Of course, nobody would have predicted in the 1998 France World Cup that Senegal will defeat France, so we need to prepare well to confront Ethiopia.
"Ethiopia of yesterday can't be same of today, that's why I almost laugh off my head when some teams said they're engaging spies on their opponents.
"I always want my side to be spied upon because a side you spied an hour ago will be a different side an hour later.
"Generally, the East Africans are known for possession of excess stamina while the West Africans are known for strength and speed, so we must deploy our comparative advantage to outwit whatever surprises the Ethiopians may come up with.
"Of course, no matter what favourable scoreline we're enjoying at any point in time we shouldn't relax until the whistle is sounded off.
"On paper people seem to believe a side gain by first playing away before wrapping it up at home, I know history has often rubbished the claim so for me adequate preparation is the key and we must not toy with preparing our team adequately for the play-off," Onigbinde said to supersport.com.
The Fifa technical instructor is upbeat Nigeria will grab one of the African slots for the 2014 Fifa World Cup in Brazil.
"I've not changed my nationality, I'm a Nigerian and will always wish my country well in every of their endeavours that include the World Cup play-off.
"We'll qualify but we must work hard to earn the World Cup ticket, it won't come cheap because Ethiopia want to be at the World Cup, too," he said.