Mum Brittany Buell uploaded photos to Facebook which show Jaxon being cuddled by Santa and falling asleep in his arms.
"Jaxon had one of his best days ever today," she wrote. "He was in a great mood all day and got to meet Santa for the very first time."
Buell continued on the post: "Tonight, we started watching Rudolph and Jaxon became very talkative with mummy.
"Lots of snuggling, lots of talking, and he's getting better each day with interacting and communicating with us, and now even playing with us. More big milestones for our little guy! #JaxonStrong"
The photos were shared on the Facebook page dedicated to Jaxon called Jaxon Strong, and they received more than 45,000 likes and more than 3,000 comments in one day.
One person commented: "These are precious and what an amazing Santa."
Another person wrote: "When I look at these, these are the true meanings of Christmas. Merry Christmas Jaxon."
Jaxon's father Brandon Buell also recently uploaded a photo of Jaxon with a "Christmas card to the entire world".
The Buell's wanted to thank those who have supported their family and sent them well wishes.