Tebow, 32, who in January got engaged to former Miss Universe Demi-Leigh Nel-Peters, shared several other photos of happy memories with Bronco, as well as his final resting place.
"I'm so thankful and humbled by everyone's support, prayers and love," he said.
"I was able to lay Bronco to rest in a really special place. Thank you all for so much encouragement. I love you Bronco, thanks for being the sweetest boy."
Fans praised Tebow for sharing such a public display of grief, with some describing it as "insanely sad" and "tough to watch".
"It's good to see men showing emotion and love," one Twitter user said.
"One of the most heart-wrenching videos I've ever seen," commented another.
Another user admitted, "You have me all choked up this morning."
Tebow received Bronco as a gift from his brother Robby in 2010 after he was drafted with NFL team the Denver Broncos, after which the dog was named.
Tebow has spent three full seasons in the New York Mets organisation.
The last two seasons had been derailed by injuries, but his inability to make the team's major league roster appeared to have put the organisation's experiment with the two-sport athlete in question.
Mets general manager Brodie Van Wagenen said he expects Tebow to start spring training on time in 2020.
Tebow and Nel-Peters are anticipated to get married by the end of the year or early in 2020.
