"Every businesses in the world is going to run on cloud eventually," Pichai said on a post-earnings call in October.
Amazon's cloud business is now its fastest-growing business, while Microsoft is banking on cloud computing to make up for slowing sales of personal computers.
Greene, a Google director for three years, will lead a new team combining the company's cloud businesses, including Google for Work, Cloud Platform, and Google Apps.
"It's evidence that Google wants to be taken seriously in the cloud and they will do what they can to make it happen and that they are here to go toe-to-toe with (Amazon Web Services) and Microsoft," Monness, Crespi, Hardt, & Co Inc analyst James Cakmak said.
Google also said on Thursday it will buy Greene's startup bebop Technologies Inc, a development platform that helps build and maintain enterprise applications. Greene and the bebop team will join Google after the transaction closes this year.
She will continue to serve on Google's board as a non-independent director, the company said.
Greene was replaced as VMware's CEO by former Microsoft Corp executive Paul Maritz in 2008.
© Thomson Reuters 2015