One Green Bean, part of Havas Worldwide, won the account following a competitive pitch that took place last month.
Lexis had held the account for more than seven years.
The agency already works with the coffee retailer on consumer projects and recently launched its first branded content and media relations campaign, ‘Costa and a Kip’. One Green Bean launched a London office in January after it won the Costa work in November 2014.
As part of the new appointment the agency will deliver press office campaigns to support seasonal activity and product launches, along with ongoing media and influencer engagement.
The account will be led by One Green Bean managing director Matt Buchanan and a team of five, reporting to Costa UK and Ireland PR manager, Kate Clarke.
Clarke said: "After an extensive pitch process, we were impressed by One Green Bean’s strategic rigor and unique approach to PR which aligns well with our ambition to create a proactive and unified content strategy delivering fresh, customer-centric ideas."