Moore's death was the first the X Games have suffered in their 17-year history.
According to ESPN, Moore's family said in a statement: "He will be truly missed and never forgotten. The family wishes to express their deep gratitude for all the prayers and support they have received from all the fans, friends and family around the world that Caleb has inspired."
The snowmobiler was attempting a backflip last Thursday during a freestyle event when the skis on his 450-pound snowmobile caught the lip of the landing area, reported the Associated Press, sending him flying over the handlebars. He then landed face first in the snow and his snowmobile rolled over him.
After some time on the ground, Moore walked off with help and went to a hospital to treat a concussion. He then developed bleeding around his heart and was flown to another hospital for surgery.
His family later said he also had a complication involving his brain.
Moore's younger brother, Colten, also crashed in the competition the same night and suffered a separated pelvis.
"It's definitely a scary thing for a sport like ours," snowmobiler and X Games competitor Levi LaVallee told USA Today. "The only thing we can do is we can look at that and learn from it and look at how we can try to prevent that.
"Other than that, you look at it, what happened to him, was an accident. He's done that trick multiple times. He's practiced. He's done everything he can to prevent that."
ESPN, which hosts the X Games, released a statement on Moore's death following questions about the safety of extreme sports.
"We are deeply saddened by Caleb Moore's passing and our thoughts and prayers go out to his parents, Wade and Michelle, his brother, Colten, and the entire Moore family. He will be remembered for his natural passion for life and his deep love for his family and friends, and he will always be an inspiration to everyone he touched in the action sports community," the statement said.
"As a result of this accident we will conduct a thorough review of this discipline and adopt any appropriate changes to future X Games."