In a post on his official Twitter page, they said: "At this time, we would like to confirm the passing of Joseph Laurinaitis aka Road Warrior Animal at the age of 60. The family is planning to release a statement later today. At this time we ask for you to keep everyone in your thoughts and prayers."
Laurinaitis was one half of the popular tag team The Road Warriors, subsequently called The Legion of Doom upon their move to WWF.
Laurinaitis' Road Warrior Animal fought alongside Road Warrior Hawk - real name Michael Hegstrand - they rose through the ranks to become two-time WWF tag team champions.
Their distinctive attire was inspired by the Mad Max series of films and, as well as being the first team to use a theme tune from a film in the WWF, they also became well known for their tandem finishing move The Doomsday Device.
Fellow WWE Hall of Fame member Hulk Hogan paid tribute to the deceased wrestler, writing: "RIP Animal, love you my brother, I know you and Hawk have a lot of unfinished business to take care of! God speed and blessings to your beautiful family, one love4Life. HH."
Tommy Dreamer, who wrestled in both WCW and ECW - now also owned by the WWE - shared a photo of Laurinaitis and said: "My friend @RWAnimal has passed away."
Road Warrior Animal's former partner Hegstrand died in 2003 from a heart attack.
They were added to the Hall of Fame for the world's largest wrestling promotion in 2011, and Laurinaitis officially announced his retirement from the squared circle in 2014.
He is survived by two children, James and Jessica, as well as his ex-wife Julie.
Rick Flair added his tribute after the news broke, writing: "I Am More Than Saddened To Hear Of The Loss Of My Good Friend And GREAT Opponent Joe Laurinaitis Of The Legendary Road Warriors.
"They Were Iconic! The Road Warriors And The Four Horsemen Drew More Money And Had More Fun And Entertained Fans Worldwide At The Highest Level. RIP"
Laurinaitis was part of a class action lawsuit filed against the WWE that alleged that wrestlers suffered traumatic brain injuries during their careers at the company, and that the company concealed their injuries.
It was dismissed by a US District Judge in September 2018.