Just for the record, there is a software (actually, a mini-distro) that does exactly the procedure arrange said in enzotib's answer:

Parted Magic

It looks like a direct conversion from NTFS to ext4, but internally the procedures are:

1. Shrink the NTFS partition


2. Create an ext4 partition in the empty space


3. Move data from NTFS to ext4 until ext4 is full


4. If NTFS is empty (all data was moved), go to step 8


5. Shrink NTFS


6. Enlarge ext4


7. Repeat steps 3 to 6 until done


8. Delete NTFS partition


9. Move ext4 partition to NTFS' orignal place


10. Trim ext4 partition to NTFS' original size

So the more occupied your NTFS partition is, the longer it will take. If it is less than 50%, it will convert in one pass, in a single shrink-copy-enlarge iteration.

Although Parted Magic conveniently automates all of this, it is still essentially the same procedures described by arrange, so it is very risky and very time consuming. Backup-format-restore is much safer and much faster.