As long as your TM backup was on Lion 10.7.2 or later, you can boot and fully restore from the TM disk.
Just plug in the TNM disk and option key boot. Pick the TM USB disk from the boot screen. Then start Disk Util and format the new disk to Mac OS Extended. Then quit Disk Util and click restore. I find it helps to consume a beer or two while waiting for the restore to complete.
Once the restore is done, reboot to your new drive and go to System Preferences' Startup Disk pane and select the new drive as the boot disk.