Andrew Marsden, Britvic's category director, selected BBH from a pitch list that included Clemmow Hornby Inge, Delaney Lund Knox Warren and BMP DDB.
The agency will begin work on the £10m account next week with a brief to create a campaign in 2004.
"BBH demonstrated a highly creative approach that captured the essence of Robinsons," said Marsden.
Britvic was forced to begin looking for an agency in April after HHCL/Red Cell ended its association with Robinsons after eight years.
The decision followed the appointment of HHCL's New York sister agency, Berlin Cameron/Red Cell, to handle Britvic rival Coke Classic.
Robinsons is the UK's number one squash brand and the number nine grocery brand, with annual sales of £200m. Fruit Shoot, a spin-off from Robinsons, is increasing sales by 66% a year, according to ACNielsen.