Question: Both of them are used: **visualization** and **visualisation**.

*Visualisation* is more commonly used in UK.  

But, *visualization* is more common in US.

What is the history of this word?   

Which is officially correct?

Answer: 
"Visualization" is the only correct spelling in American English.

"Visualisation" and "visualization" are both acceptable in British English although it is a common misconception that "visualization" is an Americanism and therefore incorrect.

Oxford resolutely prefers "ize" forms - see [visualize](http://oxforddictionaries.com/definition/english/visualize?q=visualization#visualize__19) in the British English Oxford Dictionary - and a lot of academic writing follows their lead but most mass market publications prefer "ise".

There's more information in [Wikipedia](http://en.wikipedia.org/wiki/American_and_British_English_spelling_differences#-ise.2C_-ize_.28-isation.2C_-ization.29) and an [interesting article](http://www.metadyne.co.uk/ize.html) with further references.
You've answered your own question. In the UK the following spelling is correct:

> 
> Visualisation
> 
> 
> 

In the US, the following spelling is correct:

> 
> Visualization
> 
> 
> 

This is one of a number of different spellings between British English and American English. Neither is "more correct" than the other - British English spellings are correct in the UK and not in the US.

As a learner, you know better than anyone whether knowing British English or American English is more suitable for you. If you need to learn US English, learn the US spellings. If your learning means British English is more useful to you, learn the British English ones.