"This is a dog 'appeasement' signal, called a 'submissive grin.' It is not a sign of aggression, and is identified as nonaggressive by the lack of stiff musculature and overall relaxed demeanor of the dog," behaviorist Dr. Terri Bright of MSPCA-Angell told The Dodo. "I suspect the behavior is being reinforced by the owner's attention."
Basically, the dog is reacting to his owner's excitement - which is essentially what a smile is, anyway.
Additionally, research has shown that when a dog has that relaxed, smiley look, it's usually a sign that the dog is feeling content.
This dog might not understand exactly what "say cheese" means, but he knows his reaction makes his owner happy, which in turn makes him happy - and that's all we really could want for our canine friends.