The government’s chief veterinary doc Christine Middlemiss said there will be an "amnesty", where owners will have to register their dogs and "Your dog will need to be neutered. It will need to be muzzled when out in public and on a lead and insured.
The prime minister announced the ban on Friday after the death of a man following a suspected attack.
Many have welcomed the move but others say a breed-specific ban will not work.
A 52-year-old man, named as Ian Price, died after suffering multiple injuries in an attack by two suspected American bully XLs near Walsall on Thursday.
A 30-year-old man arrested in connection with his death has been released on conditional bail, police said.
Prof Middlemiss told BBC Radio 4's Today programme: "There will be an amnesty. So people that already have these dogs - and some of them will be well socialised, well managed, well trained - you will need to register and take certain actions.
"Your dog will need to be neutered. It will need to be muzzled when out in public and on a lead and insured.
"But if you comply with these actions, and that means we'll know where these dogs are, which will be a massive benefit, then yes, absolutely you will be able to keep your dog."
Although groups like the RSPCA, Kennel Club and British Veterinarian Association argued against a breed-specific ban, shadow policing minister of the Labour Party Alex Norris on Saturday stated that he did not agree with the argument of animal charities that a ban will not stop attacks.
While the party is in support of the ban, they criticised Sunak for 'dithering' over bringing in restrictions on their ownership sooner. Sir Keir Starmer, said: "There has been a clear case for banning them for a long time.
"What I say to the Government is good, get on with it, and the sooner we can do this the better."