Burn will join an F1 grid that features increasing amounts of energy drink sponsorship by companies such as Red Bull, TNT and Monster.
"We are proud that The Coca-Cola Company [via Burn] has chosen Lotus F1 Team as the best vehicle to represent the burn brand in its most high profile partnership," said team boss Eric Boullier.
"We are excited to partner with burn to build a new and innovative model for sponsorships that will combine experiences, content creation and social media."
Burn said in a statement that it plans to incorporate "art and music in a way that will break the conventions of traditional F1 sponsorship".
The team said details of the sponsorship will be revealed in 2013 when the partnership officially launches.