Microsoft's rebranded cloud-storage service is generally and globally available as of February 19, company officials said.

Microsoft officials announced the new branding for its cloud storage service, formerly known as SkyDrive , in late January. Microsoft was obliged to change the name of the service after a l oss of a trademark battle with British Sky Broadcasting Group over the "Sky" name .

Existing SkyDrive customers don't have to do anything to move to OneDrive; their files are already in OneDrive and can be accessed by logging into www.onedrive.com with their existing SkyDrive credentials. Updated OneDrive apps for Windows Phone, Android phones and iPhones are available for download in their respective stores.

To entice new users to join, Microsoft is offering customers their first 7 GB of storage -- enough to store more than 7,000 photos, officials said -- for free. Users can subsequently purchase storage in 50, 100 and 200 GB increments. Current customers who refer friends can get up to 5 GB of extra storage. And simply by using the OneDrive camera back-up feature, users are gifted an additional 3 GB of storage.

Beyond changing the name, Microsoft is rolling out a few new OneDrive capabilities. The company is adding automatic camera backup to its Android version of its OneDrive app. And it is introducing a new monthly payment plan, allowing users to ramp up storage for specific events or ocassions.

Microsoft is not rebranding its Office Web Apps as part of today's rollout. OneDrive will continue to be the default save location for Office 365 Home Premium and Office Web Apps. Microsoft is believed to be readying an Office Web Apps rebrand to "Office Online," and is expected to simplify access to its Webified versions of Word, Excel, PowerPoint and OneNote as part of that process. Microsoft execs wouldn't comment as to when or whether this Office Online move is happening.

Microsoft also has rebranded its business cloud storage service -- formerly known as SkyDrive Pro -- as OneDrive for Business. Microsoft is not planning to share more pricing and feature specifics about OneDrive for Business until next month's SharePoint Conference 2014, however.

Update: As a few SkyDrive/OneDrive users have noted, even though February 19 was the launch date -- in more than 100 languages simultaneously -- there are still some areas where the switch hasn't happened. The SkyDrive services that are built into Windows and Office won't be updating to OneDrive until the "next major release" of those platforms, officials said. There are also some places in documentation and sites where the old branding remains and has yet to be updated.