Kurian helped in the transformation of Oracle`s products with introduction of leading suite of Cloud Services.
According to Google CEO Sundar Pichai, under Greene's leadership, Cloud has become an incredible business built on Google's decades of investment in infrastructure, data security, and AI.
Under Greene's leadership, Google Cloud has moved from having only two significant customers and a collection of startups to having major Fortune 1,000 enterprises betting their future on Google Cloud.
"We've built a strong business together -- set up by integrating sales, marketing, Google Cloud Platform (GCP), and Google Apps/G Suite into what is now called Google Cloud," she noted.
Kurian said he "is excited to join the fantastic Google Cloud team at this important and promising time".
"I'm looking forward to building on the success of recent years as it enters its next phase of growth."
Kurian stepped down from Oracle in September.
A member of Oracle's Executive Committee for 13 Years, he led 35,000-people software development team in 32 countries with an R&D budget of $4 billion.
Kurian helped in the transformation of Oracle's products with introduction of leading suite of Cloud Services, led 60 software acquisitions and Oracle's 45 Cloud data centres.
His twin brother, George Kurian, is CEO of California-based Hybrid Cloud data services and data management company NetApp and a member of the Board of Directors.