It says that Swiss authorities struck a deal with Nigeria to hand back $321m (£226m).
The agreement was signed in Abuja by Nigeria’s attorney general and a visiting Swiss delegation – and seems to confirm last year’s announcement by the Geneva prosecutor’s office about the return this money.
“We guarantee that recovered assets would be put to uses for which they have been intended,” Vice-President Yemi Osinbajo said in a statement released by his office.
The money will only be returned once its agreed exactly how this will be done.
Gen Abacha was in power from 1993 to 1998 and is thought to have stolen more than $2bn of public funds – some of it being deposited in Swiss bank accounts.
Switzerland has already returned more than $720m of the money.