The company, which operates as Esso in the UK, is looking to educate people about the role of energy in the future and about how it is developing ways of using energy more efficiently and effectively.
DLKW was appointed after a competitive pitch last year. It will work alongside ExxonMobil's incumbent agency in the US, Temerlin McClain, which developed a US ad campaign for the company in 2000.
DLKW and Temerlin McClain have been working for ExxonMobil during the past year on TV and print ads that are being rolled out in the UK this week. They will also appear in the US and Germany.
The campaign, which includes four television and press executions, focuses on the areas of energy conservation, research, future energy sources and hi-tech ways ExxonMobil has developed to explore for oil and gas.
They use the strapline: "Taking on the world's toughest energy challenges."
A spokesman for Esso said: "In the future, statistics show, the world is going to need 40 per cent more energy than today and the campaign is looking at how Esso is taking on those challenges. It is aiming to raise awareness of the company's commitment to energy in the future."
The ads were directed by Adrian Moat through the production company RSA Films.