Science Gallery has attracted more than 800,000 visitors to 18 exhibitions, ranging in theme from contagion to the future of fashion, since it opened in Dublin in February 2008.
It says the global network will be modelled on its approach to engaging young people in science, technology, engineering and maths.
The gallery's founding director Dr Michael John Gorman said it was planning eight Science Gallery hubs around the world by 2020.
They are to be developed through partnerships with universities in cities such as London and Moscow. He said the Google money would help to take the project to the next level.
The global network will officially be launched in July next year, during Dublin's tenure as European City of Science.
