The wealthy Clydebank-born star of Dragons' Den was being treated at Darlington Memorial Hospital after falling ill at the headquarters of his gym company in the town.
A spokeswoman for the Bannatyne Group said: "Everyone at the company is very concerned and upset, but we know that Duncan is a very strong person and we are confident he will make a full recovery.
"Everyone wishes him well. We'd like to thank the quick and professional actions of the paramedics who attended to Duncan and thank the staff at the Memorial Hospital for his ongoing care."
His daughter Abi said he was in a stable condition.
She tweeted: "As news is starting to spread I can confirm my dad was taken into hospital late this morning, he is stable and that's all I can say for now."
Bannatyne was later well enough to send messages from his bed to his 540,000-plus followers on Twitter, telling them: "Hi. In hospital attached to a few wires feeling tired but am sure I will be discharged tomorrow fit & well (fit as a pensioner can be anyway)"
And he followed it with: "Today was my first trip inside an Ambulance & with siren wailing. Hope it is the last. LoL"
Bannatyne, who lives on the exclusive Wynyard estate in the countryside north west of Middlesbrough, was raised in what he describes as "relatively modest circumstances".
His business interests now include health clubs, hotels, property, media and transport and he is best known as a tough-talking business angel on the BBC show Dragons' Den.
The former Royal Navy stoker began his business empire with an ice cream van, rapidly expanding that business in tough competition before setting up a chain of care homes.
On his website he says he sold that for £26 million in 1996 and his children's nursery chain for £22 million.
He has written five self-help books on becoming a success in business and managing money, was awarded an OBE for his charity works and is a vehement anti-smoker.
Bannatyne, who is a keen user of Twitter with more than 540,000 followers, tweeted this morning: "It is Monday so start the week on a positive note & stay positive".
Fellow Dragon Theo Paphitis said he had spoken to his friend in hospital and Bannatyne told him he did not think he had suffered a heart attack.
Paphitis tweeted: "In Scotland no mobile signal but managed to make contact with @DuncanBannatyne and he is well undergoing tests does not think heart attack!"
He added: "Speedy recovery we are missing you already".