As president of The Global Humanitarian Forum, Annan launched the "tck tck tck" campaign at this year's Cannes International Advertising Festival.
It has been created by Havas's Euro RSCG Worldwide network and is aimed at persuading world leaders to reach a just and binding deal at the UN Climate Change Conference, which takes place in Copenhagen in December.
At the event, Havas global chief executive David Jones presented the creative elements of the campaign and urged members of the advertising and marketing community to support the campaign and to persuade their clients to carry the "tck tck tck" symbol on their ads and websites.
Euro RSCG has created a dedicated website where visitors can upload their own personal "tck" -- a video of themselves pledging their support for the campaign, which will be added to a global petition.
The "tck tck tck" logo will be made freely available on the site in an open source format, enabling marketing agencies and advertisers to embed it into their marketing material.
Annan said: "The purpose of the 'tck tck tck: Time for Climate Justice' campaign is for the public to get world leaders to agree a just and binding agreement at the UN Copenhagen Conference in December, with climate justice at its core.
"The private sector has a key role to play. It must use its resources to take the lead in investing in more sustainable alternatives and give consumers a real choice between products."
The campaign will also comprise campaign dogtags that people can wear to show their support for the cause and a free download of the campaign song -- a special reworking of Midnight Oil's 'Beds are Burning'.
Havas's Jones said: "Our industry excels at changing people's behaviour.
"I believe that we have not only an opportunity, but an obligation to use our creativity to address some of the biggest issues facing the world like climate justice.
"To get a meaningful deal at Copenhagen requires everyone to put pressure on their leaders to agree a fair and binding post-Kyoto deal.
"This is precisely the aim of the 'tck tck tck: Time for Climate Justice' campaign, and the advertising and marketing communities have a crucial role to play."