This comes five months after BBH lost the global account for Diageo’s whisky brand Johnnie Walker to Anomaly.
Syl Saller, the chief marketing officer at Diageo, said: "BBH have always challenged us in the right way and we have always appreciated their candour, strategic leadership and creative brilliance.
"Johnnie Walker's growth trajectory was transformed by the ‘keep walking’ campaign and we are enormously proud of the work on Gordon's and Baileys.
"BBH has tremendous people who have put their heart and soul into creating great work for Diageo, and we are grateful to each and every one of them."
In a statement Diageo said the brand activity for Baileys and Gordon's will be handled in-house for the next 12 months and the work will not be put out to pitch.
Ben Fennell, the chief executive BBH, said: "We are very proud of the work that we have produced for Gordon’s and Baileys, particularly in the UK and Europe.
"The time is right for BBH to start afresh, and turn our attention to new opportunities in this dynamic category. We wish everyone at Diageo the very best for the future."