The campaign, called What Have Refugees Ever Done For Us?, is being developed by Fishburn Hedges, which was hired following a competitive pitch.
According to FH new media planner James Gordon-MacIntosh, the campaign will involve an online game, featuring a conveyor belt of inventions.
Those visiting the site (www.refugeechallenge.com) will be asked to guess which were invented by refugees.
The site launches in mid-May and will be promoted via the council and FH's mailing lists.
The campaign's title is in reference to the What Have the Romans Ever Done for Us? scene in the film Life of Brian.
Famous refugees include Albert Einstein and Sigmund Freud.
Gordon-Mcintosh said: 'We want to show refugees make a significant contribution to the UK and worldwide.'