The Glasgow-headquartered agency will support the group's NatWest, Royal Bank of Scotland, Lombard and Invoice Finance brands across the UK.
The brief is to communicate the work of the company’s employees and how this work helps customers achieve their business goals.
The agency will use its network of local hubs to service the account, with its Scottish and Manchester offices looking after Scotland, Wales and the north of England, while partnering with London-based Luther Pendragon to look after RBS in the south.
Sharon Mars, director at The Big Partnership, said the account win came following an "extremely competitive tender and pitching process, contested by major players".
In April last year, RBS group appointed Teneo Blue Rubicon to lead a reputation turnaround, in a wide-ranging brief covering all of the group's brands.