The appointment was effective from July 1, Nyanda said in a statement on Thursday.
"It is my hope that Mncube, together with the other council members, will continue to steer the regulator in the right direction and ensure that the decisions it takes are those that have a lasting effect on the lives of ordinary citizens and the Information and Communication Technology industry alike," said Nyanda.
He is a former manager in the development information business unit at the Development Bank of Southern Africa. He has also chaired the state signal distributor, Sentech.
Mncube succeeds Paris Mashile whose five-year term expired on June 30.
Nyanda thanked Mashile for his leadership "through some of the most complex issues with Icasa" since his appointment in 2005.
- Sapa