Is the drive going to be a boot drive or a storage drive? If you are simply going to pull it out of the HP and install it in the Dell as a secondary storage drive, yes, you can.
If you plan on using it for a boot drive in the Dell, things are a little different. In that case I estimate about a 50% chance of success.
What I would do:
Pull the drive out of the HP.
Install it in the Dell.
Transfer the artwork off the old drive and move it onto the new drive.
Once you are certain that you have transferred everything you need, reformat the old drive, then use it for backup.
The artwork is business, yes? You need a backup plan. You really, really do. If the drive containing the artwork had failed, what would you have done?
My...