How can I get the files from my Western Digital 1TB External Hard Drive with a new enclosure?

The usb port recently broke off my Western Digital external hard drive, so I bought a new enclosure/casing for it. The only problem is, all my files can't transfer or be accessed using this new enclosure because I used the WD smartware software that came with the western digital hard drive. The new enclosure is from Antec and it would work, but I would have to reset the external hard drive as a new drive, and I need all my files recovered. I use a mac.