There is a wide range of standard mounting kits for sliding doors, many of which can be purchased in home centers such as one of these:
The sets come with a track, trolleys for the doors and attaching hardware. Some come with trim strips that may or not work in your configuration. Stock trim cam be used instead.
These systems are designed to be attached to standard doors. There is no reason you could not use the existing doors unless they are way beyond standard weight (unlikely). You will likely need to cut 3/4 to 1+ inch from the doors, preferably from the bottom. You also will need to remove the handle and hinge hardware and fill the gaps left behind.
You can choose from a variety of options, depending on how heavy duty a setup you want (pick commercial grade if you want stronger), and how you want to place and face the track. It can easily be hidden behind your own trim work once the track is hung and the doors are in place.
It isn't hard to do, but requires some care in leveling, and an extra pair of hands helps in mounting the doors.