Unlike traditional search engines, Storm shares the commission it earns from referring traffic to online retailers with a consumer's favourite charity or organisation.
Capella said it had been appointed to help Storm "challenge the dominance of established search giants like Google".
The search engine and mobile app will be launched next month. Storm has said it will soon announce its first partnerships with household charities and other membership organisations, including Premier League football clubs.
Sam Tilston, chief marketing officer at Storm, said: "Storm is a hugely ambitious company and Capella is a partner that we feel shares that hunger to get our brand out there. We’re looking forward to working together to bring consumers a viable alternative to the established search giants."
The company is backed by investors including Kevin Taylor, the former senior executive of internet security giant Symantec, and venture capitalist Andrew Crossland. Storm was developed by Alex Kontos who founded the Waterfox browser from his bedroom back in 2011, while he was still at school.
Gareth Thomas, founder of Capella PR, said: "The search engine market is ripe for disruption and Storm has devised a really innovative and ethical way to do this. Together with the fascinating back-story of Alex, it’s a great story that we relish telling."