Celebrities including One Direction star Liam Payne, Stephen Fry and Geri Horner have backed the campaign on social media using the hastag #SaveRangTan and helped to drive people to sign the petition.
The ad, which launched globally, received over 2 million views during the first week in the UK alone, with 60,000 people signing the petition in this country.
"The response to Rang-tan has been phenomenal," John Sauven, the executive director of Greenpeace, said.
One Direction's Payne tweeted the film and got over 10,000 retweets. "It's just amazing how far and how wide the celebrities' reach is," Sauven added. "Their support for the campaign has been really brilliant."
Created by Mother London and Passion Animation Studios, the animated campaign uses emotion to appeal to a broad audience of both adults and children. This repesented a different approach than much of cause advertising.
Hermeti Balarin, a partner at Mother London said: "When you’re working on Greenpeace and cause-related briefs the natural tendency is to go a bit more aggressive and we had those ideas as well, but in this case this specific brief was about an endangered species that is very close to us.
"They’re the closest relatives we have in nature so we felt very early on that an emotional approach would work stronger because we needed empathy."
The campaign calls for brands including Nestlé, Unilever and Mondelez to keep their commitment to drop dirty palm oil from their products by 2020.
Balarin said people need to be "more responsible" and demand that companies stop using palm oil in their products, otherwise "their brands and their products won’t exist for much longer."
Voiced by Emma Thompson, the ad was directed by Salon Alpin. Greenpeace's media company was MC&C Media.