Flanagan will join the children's charity from publishing investment company Heritage House, where he is chair. He previously spent 10 years as chief executive of the Scottish Media Group and has also worked for PA Consulting, telecommunications company Nynex and Pricewaterhouse Coopers.
He will take up the role in January, when he succeeds Dame Mary Marsh, who is leaving to become director of the new Clore Social Leadership Programme, which aims to develop talent in the sector.
Sir Christopher Kelly, chair of the NSPCC, said Flanagan had "shown significant skill in managing large organisations through periods of change".
"In today's challenging times, I am confident he will continue to build on the NSPCC's proud history of helping vulnerable children," he added.
In a statement, Flanagan said: "We will need the continuing support of the public to help improve the lives of many thousands of children who look to the NSPCC when they have no one else to turn to."
Sir Suma Chakrabarti, chair of the VSO international board, said Mayne had considerable experience in the areas of change and organisational development, as well as being experienced in legal and governance structures.