If the drive is just raw data, no problem. If you have an operating system on the drive and your new computer has the same type of CPU (Intel/AMD) then you should be okay, but it will need to detect all the new hardware for the new PC.
If the drive only contains programs that were installed under another drives OS then no, the programs will not work. Applications generally make all sorts of related entries in the system registry that the OS needs to run the apps properly. In this situation you could re-install the applications easily enough, just make sure your saved files are not over written.