Windsor featured on the show as one of the professional dancers and starred on the BBC series from 2010 to 2013.
During his time on the show, he partnered with Deborah Meaden, Lisa Riley, Anita Dobson and Patsy Kensit.
His death was announced on Facebook by Burn the Floor, the dance company he founded.
A statement said: "The Burn the Floor (BTF) family has lost one of its founding members, Robin “Bobby” Windsor – who has tragically passed away. A BTF journeyman he danced with us for twenty years – including Broadway, The West End and all our crazy adventures around the world.
"His stunning image attached with Jessica Raffa defined our company, colourful, extreme and sensual. His talent, attitude, energy and personality helped create the Burn the Floor stage reputation. He leaves a void in our hearts that will never be filled, yet our wonderful memories will stay forever."
Windsor had recently been starring in Come What May, a Moulin Rouge tribute show produced by Sisco Entertainment.
In a tribute on social media, the company wrote: "His extraordinary ability to express emotion through movement captivated audiences, leaving them spellbound with every step.
"Beyond his impeccable dancing, Robin's vibrant spirit lit up the room, infusing rehearsals and performances with infectious energy and warmth.
"His laughter was contagious, his kindness boundless. His friendship was a gift cherished by all who had the privilege of knowing him. Robin, you will be deeply missed."
"Everyone who came in contact with him adored him, from his celebrity partners to his working colleagues. You will be missed old friend."
https://twitter.com/The_JamesJordan/status/1759836560990633995
Strictly judge Craig Revel Horwood also paid tribute to Windsor, describing him as "one of the kindest, gentle, honest, funny and caring people I’ve had the pleasure of knowing and working with."
https://twitter.com/CraigRevHorwood/status/1759855693556023435
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