MySQL - Changing from system tablespace to file per table

The MySQL database I am working on has the InnoDB tables and indexes stored in the system tablespace which is now > 20Gb. Some years ago I managed a MySQL database that made use of a file per table and looking to the future this seems the way to go. The documentation says that this can be done by setting “inno_file_per_table = 1” in my.cnf. Obviously I would need to back up and reload the data into the separate tables but the procedures I have seen are not that clear. Besides my database schema there are also schemas present for information_schema, mysql and performance schema which I suspect come into the equation. MySQL is running under Mint Linux and although I have seen an answer to this question under Windows I am not 100% confident on translating this to a Linux OS. What is the best way to achieve this change. It is acceptable at this stage for there to be a few hours downtime.

Thank you