RKCR/Y&R, which will handle the business from the UK, has been tasked with creating a global advertising idea.
Fallon London, the incumbent in the UK, is expected to lose its £10m UK rum account to RKCR.
Y&R pitched against Wieden & Kennedy, McCann-Erickson, Fallon and US independent Davidand-goliath, which handles Bacardi's business in the US.
Although timings have not been confirmed, the first work is expected to break next year, before being rolled out across key markets.
Stella David, Bacardi's recently promoted global chief marketing officer, and global brand director John Burke oversaw the pitch, which included presentations in London and the US.
The process, handled by AAR Partners in New York, followed a curtailed advertising review last year to consolidate the global rum brand in a single agency. Instead, Fallon was appointed to handle the UK business.
Bacardi's media agencies are unaffected by the change in creative responsibilities.
Bacardi is currently running its first UK ads since Ofcom introduced rules stopping alcohol brands associating themselves with sex. The £10m activity, by Fallon, uses the line 'The way it should B' and will air until after the festive period.