Nothing wrong in your steps, it happens to me as well, might be a bug.
But we need to install
While installing from terminal using
apt-get getting dependency errors as in the bug.(I missed the bug page, I will add the link later)
I manually installed all the
First download all
Now install in the order either from Software Centre or from terminal,
From terminal (I suggest use terminal, If you got errors use Software center)
ls #to avoid errors with file names
sudo dpkg -i [language-pack-ja deb]
sudo dpkg -i [language-pack-ja-base deb]
sudo dpkg -i [language-pack-gnome-ja-base deb]
sudo dpkg -i [language-pack-gnome-ja deb]
sudo apt-get update
If still not able to change to japanese, Again follow the procedure,
1) Hit + in Language&Region settings.
2) Find japanese or 日本語.
3) Double-click (This time should work, as shown in screenshot)
After that hit set language and set system language
You need to
restart system to apply changes.
After restart, your language settings will be changed,