Changing back up source with different os

Is there any effective way to move the files that already in My Passport (from laptop: windows) and put it back in my new Mac (os mavericks) 

is that right that I have to reformat My Passport? to HFs or Fat 32?

Should I back up manually if I format My Passport?

Thanks before

Hello,

If the drive is in Windows format (NTFS), then the Mac computer should be able to read it. You can copy the files to the Mac and then format the drive for Mac (HFS).