Tim Cook. AP It's been only four months since Google convinced enterprise queen Diane Greene to lead its fledgling cloud-computing business, but she's already scored a second huge coup for Google: landing Apple as a customer which is not good news from Amazon.

Apple has reportedly signed a contract worth between $400 million and $600 million to use Google's Cloud Platform, reports CRN's Kevin McLaughlin and Joseph Tsidulko.

It's not clear if that's the annual or total value of the contract, or if the money will be taken directly away from what Apple spends on Amazon Web Services (AWS) or not. While Apple won't quit using AWS altogether, if it is a shift in budget, this could cut Apple's spending on AWS by as much as half.

The secretive Apple has never publicly talked about being an AWS customer, but its use of it, as well as Microsoft's cloud, Azure, has been widely reported since at least 2011 and was confirmed by Apple in a security document. Apple uses AWS and Azure for parts of its iCloud services, The New York Times reported.

Last month, Morgan Stanley analyst Brian Nowak estimated that Apple spends about $1 billion a year on AWS. Nowak believes that Apple was planning on cutting those costs with AWS sooner or later as it builds new data centers. Besides iCloud, Apple runs huge data centers for iTunes and the App Store.

Convincing Apple to try Google's cloud is said to be the work of Greene, who has been busy building more partnerships for Google and wooing big names.

Diane Greene. Google This win is especially impressive given Google and Apple's cantankerous history over the mobile-computing market the past few years.

This is Greene's second big score: Spotify also announced last month that it's using Google's cloud. Spotify is also an AWS user.

Meanwhile, Dropbox is also engaged in an exodus from Amazon's cloud empire, reports Wired. Dropbox isn't moving to Google. It's grown big enough to build and run its own data centers, however we understand that Dropbox is still using AWS in certain instances, like for international customers.

So Google is working hard to shrug off its status as the No. 3 cloud vendor, behind Amazon and Microsoft.

Top Google cloud executive Urs Hölzle says that, by 2020, Google could be making more money from cloud-computing services than it does from advertising.

Google could not be immediately reached for comment.