Rival agency Resonate was hired after a three-way pitch against M&C Saatchi and the Launch Group, which had promoted the supermarket's flagship corporate social responsibility scheme for five years.
Computers for Schools 2008 will launch in March - its 17th year of operation.
Resonate MD Michael Frohlich said the agency's brief is to promote the scheme as being 'bigger than just computers', highlighting the fact that vouchers can now be used towards other equipment, such as musical instruments, reference books and digital cameras.
Resonate may also have to deal with controversy about the scheme, because Tesco has in the past been accused of spending too small a proportion of its profits on computers.
Last week, Launch was appointed to a new project for Tesco's Healthy Eating range (PRWeek, 18 January 2008).