What procedure is needed to reshape my jaw into one that looks like this?

While your pictures are not the best to do computer imaging, it appears you would need a combination of a sliding genioplasty (to bring your chin forward and to vertically shorten it as it is too long) as well as jaw angle implants. Better quality pictures would be needed to determine how these change would look on your face.

 Hi, I have performed many facial shaping procedures using dermal fillers, silastic facial implants (cheek, chin), liposuction and/or facelifts for over 30 years.  Following my beauty principles, men (like the model examples provided) look chiseled and handsome with angularity in the cheeks, chin and mandibular angles.  From the photos, your cheeks are flat in the front, the chin is weak as are the mandibular angles.  The following procedures would create a more ruggedly handsome face.
Cheek augmentation with cheek implants to add angularity to the cheeks and mid face.  Liposuction can be combined to reduce any excess fat to further shape the cheeks and face.Chin augmentation, using a chin implant, to add projection to the chin creating harmony and balance to the lower face.  I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut bone segments).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  In my opinion, you are a good candidate for chin implant surgery.  Augmentation of the mandibular angles using a dermal filler (jaw implants have too many unwanted side effects IMHO) to add volume, angularity and flare to the jaw line. These procedures would have no effect on your occlussion (how the upper and lower teeth come together) nor will braces affect the facial features decribed above.  
Hope this helps.