Swati Dlamini and Zaziwe Dlamini-Manaway say they have the former South African president's blessing.
The 13-episode series, already filmed, follows the two women as they try to promote the family's legacy while juggling motherhood in Johannesburg.
In interviews this week, they said their 94-year-old grandfather was doing well following his recent health scare.
They said he is "happy and healthy", and produced a photograph taken at the start of the month in which Mr Mandela holds his youngest great-grandchild - Zaziwe's one-year-old son - on his lap.