Give that it’s 100% MySQL compatible, you can update in-place (nevertheless it is recommended that do a backup of your data first). The steps are roughly adapted from here.

1. Go to the MariaDB repository configuration tool and generate your .list file (wondering what’s up with the 5.5 vs 10.0 version? See this short explanation). You don’t know the exact Ubuntu version you’re running? Just use lsb_release -a.
2. Save the generated file under /etc/apt/sources.list.d/MariaDB.list as recommended and do an sudo aptitude update. You should see an output complaining about some public keys.
3. Do sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 0xCBCB082A1BB943DB to add those keys (replace the last number with the one you saw in the previous output).
4. Issue sudo apt-cache policy mysql-common and you should see mariadb as an upgrade option.
5. Finally do sudo aptitude upgrade mysql-common libmysqlclient18 and watch your MySQL database being transformed into a MariaDB one and all keeping chugging along just as usual!