At the launch on Tuesday, officials said the project – which also includes the provision of clean water – will help in tackling the spread of diseases.
It will be carried out over the next three years with support from the private sector, authorities say.
There are also plans to expand the project to cover the country’s 36 states, Nigeria’s water resources minister said.
Nigeria is Africa’s most populous country and its capital is one of the fastest growing cities on the continent – with increasing pressure on limited water and sanitation facilities.
In the city 39% of residents defecate in the open, according to official figures.
The West African country is also expected to host a world toilet summit later this year.
One of the targets of the United Nations Sustainable Development Goals is to eliminate open defecation by 2030. But experts say progress has been slow.