In order for you to transfer from your home to your host university, you must apply for an Erasmus+ exchange during your first study semester.
You will be assigned a place at the host university and have good chances to get an Erasmus scholarship (however, there is no guarantee).
Note that there are different Erasmus application deadlines at each home university beginning from December to mid February.
Please check the information on the respective websites of your home university regarding the application procedure and deadlines. In case of questions, contact the office in charge.