Yup, they can be converted. Consulting the Regal web site, one finds that: "All Regal vises are shipped as right hand vises. Converting the right hand vise into a left hand vise is a very simple procedure that only takes a few minutes. On the under side of the vise you will see a hex nut in the ball that holds the jaw handles in place. Simply loosen the hex nut with a 7/64" hex wrench and swing the jaw handle to the other side. Tighten the hex nut and you are ready to tie from the left hand position."
Refer: http://regalvise.com/index.php/Customer-Service.php