Piper, whose real name was Roderick George Toombs, was inducted into the World Wrestling Entertainment (WWE) Hall of Fame in 2005.
Nicknamed "Rowdy," Piper was known for wearing a kilt outside the ring, entering to bagpipe music and his frenetic, big mouth.
He teamed with Paul Orndoff in the main event at the first Wrestlemania in 1985, where they lost to Mr. T and Hulk Hogan, with whom Piper had a sustained ring rivalry in the 1980s.
"He was my best friend. He is a legend. God's gain is our loss. May his family find peace in this time of need. My love forever -- HH," Hogan said in a written statement.
Piper, born in Canada of Scottish heritage, wrestled in World Championship Wrestling before returning to the WWE in 2003.
"Roddy Piper was one of the most entertaining, controversial and bombastic performers ever in WWE, beloved my millions of fans around the world," said WWE Chairman & CEO Vince McMahon. "I extend my deepest condolences to his family."
During his years with the WWE, the wrestler sometimes hosted an interview segment called "Piper's Pit," in which he often antagonized another wrestler. In a memorable 1984 confrontation, he ended up cracking a coconut on the head of Fijian wrestler Jimmy Snuka, then rubbing a banana in his face.
During his feud with Hogan, Piper once attacked two Hogan allies, singer Cyndi Lauper and wrestling manager Captain Lou Albano, and while Lauper lay on the ground, grasping Piper's leg, Piper kicked her.
At WrestleMania 2, Piper's boxing bout with Mr. T ended when Piper pushed down the referee and body slammed the actor.
According to the Internet Movie Database, Piper had appeared in many television shows and movies, including the cult classic "They Live," directed by John Carpenter.
Carpenter mourned his friend on Twitter.
"I'm devastated by the passing of my friend Roddy Piper," Carpenter wrote. "Great wrestler, underrated actor, dear friend, Rest in peace, Rod."
Wrestler Chris Jericho said on Instagram: "Sorry to hear of the passing of my friend and Wrestlemania rival #RoddyPiper. One of the greatest who ever lived, but more importantly a legit sweet family man with a good heart. God bless you Rod....See you on the other side. #RIPHotRod."