The agency won the business following a pitch against Carat, Manning Gottlieb OMD and Brilliant Media.
Universal McCann retains its existing press, radio and TV buying business and adds digital, search and outdoor work previously held by Carat.
The Carbon Trust was set up by the government in 2001 as an independent company. Its mission is to accelerate the move to a low-carbon economy by working with organisations to reduce CO2 emissions and develop commercial low-carbon technologies.