The Northern Irishman passed away peacefully at his home in Wombourne on Wednesday.
He had two spells in charge through 1985 and 1986, after previously serving the club as chief scout. Both of his sons, Campbell and Cavan, played for Wolves. He is survived by them and wife Jeannie.
And Cavan wrote on Facebook: "Apologies but no other way to contact everyone. Unfortunately, my dad passed away last night/yesterday at home.
"He was in good spirits the last time I spoke to him. We will be organising the funeral/memorial at Trysull in the next month for all that can make it. Thanks for your condolences in advance.”
Chapman's reigns came in the darkest period of Wolves' history.
He first took over on an interim basis, after Tommy Docherty was dismissed in July 1985, and was put in charge again later that year after Bill McGarry's return to the club lasted just 61 days.
Chapman was unable to prevent Wolves from dropping into the fourth tier for the first time in their history, and he left the club in August 1986 – succeeded by Brian Little.
Dean Edwards, one of the many players signed by Chapman while at Wolves, posted on Facebook: "Gutted is not the word. My thoughts go out to his family and my good friends Campbell and Cavan. RIP Sam."
In another comment, Edwards added: "He was not only a great manager but a larger than life character who always had a smile on his face. He was lovely to be around and was unbelievably funny. He will be missed by many.”
Fellow ex-player Jon Purdie paid tribute to Chapman too.
"Sammy was a charismatic character with a great sense of humour," said Purdie.
“He gave me my debut at the age of 18 and although we didn’t have a great team, he had such a great personality that we all wanted to play for him.
“He worked tirelessly for the club under very difficult circumstances under the Bhatti brothers. I think he deserved more credit for keeping the club alive during that dark period of the club's history.
“I heard that he wasn’t very well some time ago and went to visit him at home out of my respect for him. I was dreading seeing him poorly, but true to form he was full of life and we spoke at length about football and some of the stories from our time together.
“I only have fond memories of him and we have lost a true football man and a great character. My thoughts are with all his family.”
Chapman's sons, Campbell and Cavan, made 57 and one appearances for Wolves respectively.
His own playing career included spells at Mansfield and Portsmouth and a Northern Ireland B cap.