Twist had married Harry's mother, Anne Cox, in 2013; Harry acted as the best man at their wedding. The couple had just celebrated their fourth anniversary earlier this month.
Harry's One Direction bandmates reached out on social media with touching messages of support. "Such an extremely sad day for us all who knew Robin," Liam Payne wrote on Instagram. "What a kind, gentle and beautiful soul, a true rarity to find in today's world."
Niall Horan added, "Very sad to hear about the loss of Robin ... he was the nicest, kindest, most generous, hilariously funny guy you'll have met. He always had a smile on his face even when he was battling the terrible illness."
And on Twitter, Louis Tomlinson sent his love to Harry's family.
Harry's fans have also provided an outpouring of support on Twitter and Instagram under the hashtag #RIPRobin.