"Cannot wait to spoil our boy," Kailyn Provin,Fox's fiancée, wrote in a post on her Instagram story, which Fox also shared on his account.
The Chargers also congratulated Fox's dog on Twitter.
Fox's grandmother, Sandy Fox, breeds French bulldogs and gave Winston to Morgan when the dog was a puppy.
"We raised him and she said, 'Can I show him, we just like to show dogs?'" Morgan Fox explained. "And he just started winning and winning and kept winning."
Winston, who is three years old, came in second place in the Westminster Kennel Club Dog Show in June.
"When he was really young, he would win, but not all the way," Morgan Fox said. "And then all of a sudden, he just started winning the big ones, bigger and bigger, and we were like, 'Oh yeah, he's the real deal.'"
When Winston isn't traveling for dog shows or training with his professional handlers, he lives at home in Southern California with Morgan and Kailyn, who treat him like a normal hound.
"He plays with our other dogs, he plays in the backyard, he hangs out and is a menace around the house," Morgan Fox said. "He just runs around. Frenchies have all this energy."
Fox, a sixth-year pro, is attempting to embark on a winning streak of his own.