BMB, which also handles the Agriculture and Horticulture Development Board's British Pig Executive brief, won the account after a pitch against other agencies on the AHDB roster.
TBWA\London previously handled the EBLEX ad business, having won the account in a pitch against DDB UK in February 2009.
Other AHDB roster agencies include Archibald Ingall Stretton, DDB UK, JWT London and The Red Brick Road. The body created the roster in 2010.
Recent work for EBLEX has included a print campaign highlighting quality standards, while TBWA created an iPhone app that encouraged users to cook a virtual steak.
EBLEX also invested in TV sponsorship through a deal last year with UKTV to support the food programme Matt And Allegra's Big Farm.
The body is still well-known for its "Beefy" and "Lamby" characters based on the cricketers Sir Ian Botham and Allan Lamb, introduced in TV spots by Leo Burnett in 2005.