The Publicis-created campaign, which will roll out across markets in Europe, the Middle East and Africa this week, aims to raise awareness of HP's new range of home-based print products.
The EMEA activity is the first time HP has dropped TV advertising, and instead used press ads, outdoor posters, online advertising and in-store activity.
A dedicated has also been created, which allows visitors to download free greeting cards, CD labels, paper dolls and other content inspired by Stefani.
Rebekah O'Flaherty, vice-president of marketing at HP Imaging and Printing Group, EMEA, said: "People no longer rely on having a PC with a printer attached to it, but instead use digital devices to create and share content over the Internet.
"Our aim is to inspire our customers with new ideas to express themselves and to provide them with the necessary tools to mash, create and publish exciting new content, online."
The global campaign will be expanded in 2008 to reach the enterprise, graphic arts and small to medium-size business communities.
The activity is part of a business strategy called 'Print 2.0', which aims to make it easier to print from the web and create digital content.
The company is also developing a next-generation digital printing platform which is aimed at increasing print speeds and lowering the cost of printing for high-volume commercial markets.