You can just manually move the files yourself. However if you leave the backups directory in the data directory, it will show up in MySQL as a defunct database (i.e. the “lost+found” you see often). In MySQL 5.6.3+ you can use the ignore-db-dir option to ignore the backups directory, but if you are running 5.5 then I’d figure out how to store your backups somewhere else preferably.