The striker, whose goals led the club to their first title back in the 1953-54 season and provided the catalyst for the famous victory over Honved in 1954, died at a nursing home in Kidderminster yesterday at the age of 86 following a long battle with vascular dementia.
In his career, he made 230 appearances for the club, scoring 114 goals between 1945 and 1957.
Former players and family members have paid tribute to the Yorkshire-born footballer, who retired following a knee injury in 1957.
Mr Moxey paid tribute to the former number nine, calling Roy 'one of the club's most iconic footballers'.
He said: "Everyone at Wolves was deeply saddened to hear of the death of Roy Swinbourne - a true Wolves great.
"Roy is one of the club's most iconic and revered footballers and he's left an everlasting mark on the club's history.
"He was the hero of the famous floodlit game versus Honved, which many fans say is the club's most famous victory.
"Therefore, it was no surprise when, in 2011, he rightfully took his place in the Wolves Hall of Fame.
"Despite his career being cruelly cut short by injury, he was never bitter.
"He looked back on his career with great pride, as he should have done, playing such a key part in a golden time in Wolves' history.
"In later years Roy bravely battled illness supported by his devoted wife, Betty.
"Our thoughts are with Betty, and the rest of Roy's family, during this sad time."
His wife of 62 years, Betty Swinbourne, 83, said: "He was the most kind man you could ever think of.
"He loved his family and friends, loved people and was wonderful with children.
"He had a smile that made everybody love him back and he was such a warm soul."
After being forced to retire from the game in 1957 due to a knee injury, Roy worked as a rep for Wolverhampton tyre giant Goodyear, before starting his own successful Midlands-based tyre business.
He moved from his home in Kinver to The Shrubbery nursing home in Kidderminster around six years ago as his illness began to escalate.
His wife added: "Everything he turned his hand to in life he was a success at, whether that was football, work or his family.
"I am probably even prouder of Roy for making such a success of his life after being forced to retire from the game than I am of his achievements in sport.
"He was in a bad way when he had to stop playing, to pick himself up and do so well showed great strength."
Ron Flowers, who played with Roy during one of the clubs most successful eras, said: "Roy grew up just a village down from me and we both came through the Wath Wanderers set-up.
"I had heard a lot about him before I even moved to Wolverhampton, his brother would always be talking about him and the Wolves.
"He was a true gentleman, a perfect bloke and a really good influence to people around him.
"On the pitch, he was just the kind of player you wanted on your team, especially away from home when it was time to separate the men from the boys."
Wolves players will wear black armbands in memory of Roy during today's league game away at Charlton.