The agency won the account in a pitch, which kicked off in February, and will now develop a campaign to reassure consumers that Google is a safe brand that they can trust.
The search giant has moved to allay public fears after coming under criticism over the past year over the way it handles privacy and data issues.
Last year, it emerged that Google faced a possible fine for breaching privacy laws after admitting that it had collected people's private data while compiling its Street View project. It was also the subject of an anti-trust investigation by the European Union, following complaints by Microsoft that it abuses its dominance in online search.
In recent years, Google has worked with a number of agencies on a project basis, including Glue Isobar, BBH Labs and Essence. The agencies were appointed to work on activity to support Google's Chrome browser. OMD handles its UK media planning and buying.
Google also works with AKQA San Francisco on its US advertising campaigns.
Recent work for Google included a campaign last year, through Bartle Bogle Hegarty, which produced two films for Google Chrome to launch on YouTube, building on an original campaign called "Chrome Features".