The TV star died on Saturday, his longtime agent and family friend Pat Lake-Smith said.
She said in a statement to the PA news agency that the “ultimate entertainer” had been recovering from the fall when he died.
“It is with great sorrow that I confirm that Des O’Connor passed away yesterday,” she said.
“He had been admitted to hospital just over a week ago, following a fall at his home in Buckinghamshire.
“He was recovering well and had been in great spirits, visited by his family – in accordance with hospital lockdown regulations – and looking forward to going home.
“Unfortunately yesterday evening his condition suddenly deteriorated and he drifted peacefully away in his sleep.”
O’Connor presented his own prime-time TV shows for over 45 years.
He was known for shows like Today With Des And Mel and Des O’Connor Tonight.
His agent said: “Des, who was 88, was so well loved by absolutely everyone. He was a joy to work with – he was talented, fun, positive, enthusiastic, kind and a total professional.
“He loved life, and considered enthusiasm almost as important as oxygen. He adored his family – they were everything to him. He is survived by his wife Jodie, their son Adam and his four daughters, Karin, TJ, Samantha and Kristina.
“Jodie’s world is shattered, she and Adam and Des’s daughters are hurting more than you could possibly imagine.
“Des was the ultimate entertainer.
“He loved being on stage – entertaining a live audience. He always said the sound of laughter was like the sound of heavenly music.
“He had a fabulous international TV career, presenting his own prime-time TV shows for over 45 years. On stage he starred at almost every leading venue throughout the world.”