The DfES campaign is part of a drive to ensure that the UK's workforce is skilled enough to compete globally.
The budget will be around £100,000 and it will run to the end of the year.
Led by senior consultant Emma Light, the specialist corporate agency is charged with establishing higher education as a means of meeting employers' skills needs.
It will encourage more universities to develop programmes that meet the education and training needs of employers.
The campaign will run alongside a Learning & Skills Council drive launched earlier this month to promote training and learning.
The latter campaign launches in the summer and ties together the LSC's service-specific publicity, targeting consumers and employers. Hill & Knowlton teamed up with ad agency Leo Burnett to clinch the two-year brief earlier this month (PRWeek, 13 April).