MindShare's first work for the council, which has a £20m annual budget, will be a campaign promoting Train To Gain, a service launching in September to help employers access training schemes.
Funded by the Department for Education and Skills, the body's remit is to make English business more competitive through vocational education.
With a budget of more than £9bn, it oversees non-university adult education schemes, including modern apprenticeships and adult learning grants.
MindShare, which recently won the planning brief for a government campaign to tackle benefit fraud, pitched against MediaCom, Manning Gottlieb OMD and Starcom. The review was handled by the COI.