Google Japan recently announced on its blog that the Japanese Input Method, which has been in development since last December, is officially out of beta. There is actually an open-source version of this input method called Mozc.
Install iBus-Mozc in ubuntu using PPA
Open the terminal and run the following commands
sudo add-apt-repository ppa:japaneseteam/ppa
sudo apt-get update
sudo apt-get install ibus ibus-mozc ibus-gtk
Once you restart, you should then see in the applet menu the keyboard icon. Under the setting, you can add Japanese > Mozc to enable the input method.