The feature is coming in an update rolling out now.
An update (5.1.0) allowing you to transfer your Wii U data to another Wii U is currently being rolled out by Nintendo.
As outlined on Nintendo's support page, the feature will only work with two working and present consoles (no dice if it's broken or lost), and will transfer users, Nintendo Network IDs, save data and downloaded content from one to the other. Once the transfer is complete, the source Wii U will be formatted.
One presumes this feature won't be too useful in the immediate future, but might have some worth if different models are released down the line, or if you're looking to upgrade from the basic to deluxe model.
Check out all the details on Nintendo's support page.
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