The agency was appointed after a pitch, and will now work on a series of projects for the DIY retailer to help promote its sustainability and environmental credentials.
It is thought that B&Q is keen to put more emphasis on showcasing itself as an environmentally conscious company, and will put the message at the heart of its marketing communications in 2012.
B&Q spends around £55 million on advertising each year, according to Nielsen. The bulk of its advertising is handled by McCann London, which won the business after a pitch in July 2009.
Green commented: "We love working with the modern mainstream, and that's the heartland of B&Q. We're thrilled to be working with one of the UK's most famous and loved brands."