The trainer's death was announced on social media this morning.
One of Britain's most renowned boxing trainers, the Irishman trained four world champions including Johnny Nelson and Naseem Hamed.
He died peacefully in the city's Royal Hallamshire Hospital at 7.40am this morning.
A former professional boxer himself, he set up a boxing club in Wincobank to help young people in the local community and the gym became a breeding ground for some of Britain's most successful boxers.
He trained Prince Naseem Hamed from childhood and Herol 'Bomber' Graham, regarded as Britain’s best boxer never to win a world title, was also a product of the gym.
World crusierweight champion Johnny Nelson, who was trained by Ingle, was among the first to pay tribute, writing on Instagram: "On this 1 occasion I am using social media to inform people a good good man has left this earth today.
"A good friend. A good father figure.. AND THE BEST TRAINER IN THE WORLD"A person's worth is measured by the worth of what he values - Marcus Aurelius... BRENDAN INGLE MBE RIP"
Born in Dublin in 1940, he was awarded an MBE in 1998 and also has an honorary doctorate from Sheffield Hallam University.
The gym is now run by sons Dominic and John Ingle and continues to produce quality fighters such as Kell Brook.