Is the Wii Fit U board compatible with the original Wii?

I have Googled this for ages and can't find an answer.

I know that the Wii Fit board is compatible for the Wii U, but how about the other way around: original Wii & new Wii Fit U board?

Just to make things clear: there is no such a thing as a "Wii U Balance Board"; there has only ever been one model of the Balance Board. The one you get in the Wii Fit U console bundle is actually the same board that was sold with the original Wii Fit. Some online retailers may erroneously call it "Wii U Balance Board", while it's actually "Wii Balance Board" or just "Balance Board".

Here is a link to Nintendo's website regarding the Wii Fit U Bundle. As you can see, it contains the one and only Wii Balance Board, since there are no other versions of the device.

So, to answer your question: the Balance Board you get with the Wii U bundle is fully compatible with the Wii.