How do I import Time Machine backup from different (dead) iMac to new iMac

I recently bought a new iMac (OSX 10.9.4), but before I could transfer my files from my old iMac (2008), the old one died. It won't boot up at all. Fortunately, I have my Time Machine backup (from the old Mac) on a LaCie external hard drive.

Is it safe to just plug the LaCie into the new iMac? What will happen? Will it allow me to import my files? What about my iTunes music? And my photos? I'm afraid the new Mac will automatically reformat the hard drive for its own Time Machine, and my files will be lost.