The agency has been hired to lead a brand strategy and PR campaign for the ethical energy firm.
Unity will help to relaunch Ebico by working with the company around its messaging and brand strategy before moving on to a creative consumer campaign during 2015.
The campaign will target consumers with a social conscience as well as people trying to escape fuel poverty.
Unity’s co-founder Nik Govier and senior account director Katreena Dare will lead the account.
Govier said: "Unity is an agency that was founded around three core beliefs: of doing the right thing creatively, commercially and ethically. Ebico is one of those rare brands that links directly to all three pillars."