BBH won the creative assignment for the mobile phone joint venture between Swedish company Ericsson and Japanese firm Sony at the end of 2001, following the creation of Sony Ericsson in August of that year.
The agency beat Saatchi & Saatchi, which handled Sony's mobile products in the UK, to win the account.
BBH's decision to resign the account is said to stem from a disagreement over creative direction.
In a statement, BBH said: "This decision is based on differences of opinion regarding the creative direction of the brand. The decision remains amicable and both companies wish the other every success for the future."
BBH has carried out several global advertising campaigns for the mobile phone brand since 2001, with the most recent ad breaking earlier this month.
Ana Ivanovic and Daniela Hantuchova starred in the television ad to back the launch of Sony Ericsson's K800 and K790 Cyber-Shot camera phones.
The ad, which was the latest in the "never miss a shot" campaign and part of a global push, was written by John Hegarty.
It featured a tennis match between the two female stars using the roof-tops of tall buildings as their court.
BBH's success while working for Sony Ericsson contributed to the agency winning the Best Creative Agency at the IPA's Best of the Best awards in February 2005.
The 拢30m international media planning and buying account for Sony Ericsson is held by WPP Group's Mediaedge:cia.
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