The bank will not directly replace Wheldon, who will retire at the end of March, but will recruit a director of marketing. RBS is rebranding as NatWest Group later this year.
Prideaux, who will join the banking group later this year, currently works at Aviva, where he has been group comms director since 2010. Prior to Aviva, he was a financial services partner at Brunswick.
Prideaux will report to RBS Group chief executive Alison Rose and will join the executive committee of NatWest Holdings.
Rose said: "As we enter a new era for this bank, it is vital that we clearly and effectively communicate with our customers, colleagues and wider stakeholders so they understand the steps we are taking to build a purpose-led bank.
"Nigel will have a crucial role to play in leading that agenda, and his insight and experience will make him an invaluable addition to the senior leadership team."
Prideaux said: "It’s an exciting time in the bank’s development as it focuses on becoming a purpose-led organisation, supporting its customers and making a positive contribution to society, and as it continues to improve its financial performance.”