Bailhache, who will start at RBS in February, left HSBC this week. In his new role he will report to RBS Insurance chief executive Paul Geddes.
He replaces James Murray, who left to join Fleishman-Hillard last week in the newly created role of MD for corporate comms, public affairs and financial services.
Bailhache joined HSBC in September 2010 from FTI Consulting (then FD), where he was an MD in its financial services division.
Before that he was a financial and business journalist, including City editor of The Business.
Geddes said: 'Rob's experience will be invaluable as RBS Insurance prepares to separate from the RBS Group in 2013.'