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.
She said: "It is with great sorrow that I confirm that Des O'Connor passed away yesterday.
"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 first fronted his own show in 1963, while the success of his singing career saw him sell 16 million records and spend 117 weeks in the top 10 of the charts.
The four-times married star appeared on stage around the world, including hundreds of shows at the London Palladium.
He had his own US TV programme and his chat show Des O'Connor Tonight was a British television staple for a quarter of a century.
He also hosted Channel 4 quiz show Countdown with Carol Vorderman, with the pair bowing out together in 2008
Melanie Sykes, who fronted Today With Des And Mel alongside O'Connor, paid tribute to him saying it was an ‘education and a privilege to work with him’.
She wrote on Instagram: "Des had the softest hands of anyone I ever met and the kindest of hearts.
"He had talent in every fibre of his being and was stubborn as a mule. He was the full ticket as a friend and colleague.
"When he chose me to be his co-host on the 'Today' daytime show it was one the greatest days of my professional life. It was an education and a privilege to work with him for the years that followed.
"We worked long hours but always laughed lots, not least because when it it was showtime he would always tell me I looked like robbers dog! These years I will never forget and nor will I forget him. Darling Des you will be forever missed. Melanie x".
TV star Kate Robbins said Des O'Connor was a ‘true pro and a gorgeous person.’
She tweeted: "I'm so sad to hear that the wonderful Des O'Connor has died. He was a true pro and a gorgeous person. My love to Jodie and all his family at this sad time. Rest in
peace Des. You are sorely missed already #RipDesOConnor".
Top Gear presenter Paddy McGuinness tweeted: "Such sad news. Des O'Connor was never afraid to laugh at himself and that was part of his charm. Whether it was Eric Morecambe ridiculing him, or Freddie Starr smashing his studio set up, Des always laughed along. Another part of my childhood telly viewing gone. RIP Des O'Connor".
Comedian Tommy Cannon, 82, said he would "always remember him... like a best pal".