The campaign will be directed at NGOs, employees and consumers, according to Starbucks vice-president of public affairs Anthony Sprauve.
Starbucks held talks with five agencies in a two-month search before picking Cone.
Cone has relinquished its Dunkin’ Donuts account to avoid a possible conflict in representing the competitors.
Sprauve said: ‘Cone has in-depth knowledge of the coffee industry from its proven work with Dunkin’ Donuts.’
Cone said it would put seven people on the account.
Sprauve said a central message of the campaign will be ‘how Starbucks buys all its coffee in a responsible, sustainable manner’.
Major coffee processors have been heavily criticised by some groups for not doing more to promote fair-trade coffee, which pays farmers in developing countries living wages in exchange for their crops.