All proceeds from the sale, at Halls auctioneers in Shrewsbury, will go to the Jayne Sargent Foundation, which provides a range of support services for people in Telford living with cancer.
Former super-middleweight champion Richie, who lives in Telford, said he was delighted to be able to help the group, having seen at first hand how the money will make a difference.
"I'm really pleased about that," he said. "I have got to know a couple of people working for the charity, and I have been most impressed.
"They are all volunteers who freely give their own time to others, and that is really important.
"I'm really pleased to help them, the money will bring many benefits, and the auction will also raise awareness of what they do."
The foundation's Sara Bennett said: "As a small local charity it means so much to us to have Richie’s help in raising awareness and funds.
"The money will be used to help people dealing with cancer in the Telford area with our twice a month meets providing information, support and friendship at Meeting Point House in Southwater."
She added that Richie was an active supporter of the charity.
"We are so grateful to Richie, a friend of Jayne Sargent Foundation for supporting our charity which helps people dealing with cancer in Telford.
"We enjoy Richie’s company when he comes to our charity meets and even makes us all coffee."
Richie got Fury to sign the glove during a sportsmen's dinner at Cannock in the summer, where he was interviewing him on stage.The lot also included a programme from the event.
Over the past three years Richie has raised thousands of pounds for Shropshire cancer charities through regular auctions he holds in memory of his father Len.