Andrew McGowan, 35, pleaded guilty at Liverpool Magistrates Court to being responsible for the dogs, which weigh up to 11 stone and left the toddler with 'life changing injuries'.
Her aunt, who was also looking after two other children who were unharmed, fought off the attack and ran to the front of the house carrying the toddler and screaming: 'The dog's got the baby'.
The child was mauled on the face, neck and body by the animals who were kept in an adjacent garden but got through a hole in the fence, one of her relatives said.
Her family have been by her bedside in Alder Hey Children's Hospital, where she is still receiving treatment after undergoing an operation.
McGowan has been bailed, on the condition he does not keep any more dogs, but faces up to two-and-a-half years in prison when he is sentenced on June 6 at Liverpool Crown Court.
McGowan, from Toxteth had been breeding a large number of dogs (reports say he had 11 dogs on the property), which were kept in an 'insecure' pen.
He repeatedly glanced over to the little girl's father, who struggled to hold back tears, as the charges were read.
Two of the four dogs that attacked the girl have already been put down.
The dogs were named as Rogue, Pea, Hero and Ferrea, in the charges and identified as an 'American Bully' breed.
This is basically a hybrid dog - they've mixed a Pit Bull with American Bulldogs to create this new dog. Similar to Yorkipoos, Goldendoodles, Puggles, etc. They call them American Bullys, but they're just big Pit Bulls.
Dressed in a black jacket, McGowan covered his face as he left court this afternoon, with what appeared to be a dog lead hanging out of his pocket.
A relative of the girl said their family have been heartbroken by the attack.
They said: 'I couldn't believe it, that something like this could happen to such a tiny beautiful little thing. We're on our way to the hospital now to see how they're doing.'
Another family member said they were 'shocked and devastated'.
Merseyside Police have confirmed that there were 11 of the animals in the three-bedroom, mid-terraced property next door.
The youngster was playing outside with a four-year-old and a six-year-old, who witnessed the mauling but were uninjured.
Her cousin said that a dog 'grabbed' her by the head after 'jumping through the fence' and told Mirror Online: 'She's lucky to be alive'.
While it is not an offence to own one, it is to have a dog dangerously out of control in a public or private place.
And he said the attack could have been even more serious but for the intervention of the girl's aunt.
A family member who didn't wish to be named, speaking en-route to the hospital, said the family were 'devastated' by what had happened to the tot.
She said: 'The whole family are devastated by what's happened.'
Another family member who didn't wish to be named said they were 'shocked and devastated'.
She said: 'We're devastated by it all and are going up to the hospital this afternoon to see her.'
Mother-of-one Samantha Morris who used to live on Cockburn Street, but now lives a few streets away, said she was 'horrified' by what had happened.
Ms Morris, a sales assistant, said: 'It's horrible, it's the first time I've heard this kind of attack happening around here. It's shocking.
'I have a little boy who's five and I don't let him play out in the street because of the cars driving by, and now this.'
A grandmother who lives the adjacent street, who wished to remain anonymous, said: 'It's sickening, I hope they put the dogs down. There are quite a few dogs in the area. 'It's scary, there's loads of children around here, it makes you scared to let them out. It makes me feel scared and frightened.
'It's normally very quiet around here, a few kids out on their scrambler bikes now and again but quiet apart from that.'
Another man from the same road, who didn't wish to be named, said: 'It's really bad what happened to that little girl. When you keep dogs like that, what can you do?
'This is usually a quiet street, nothing like this goes on here.'
Supt Wiggins said suspicions the owner was breeding the dogs had also been a line of inquiry for police.
He said: 'There were 11 dogs in that property yesterday, either in the back garden or in the house. We know five of them were adult dogs and six of them were puppies. We have had them assessed today and we can confirm they are not a banned breed.
'There were three young children playing in that garden at the time, aged two, four and six and that the 57-year-old auntie who was in that property, was in the garden at the same time.
'Now she's managed to get the two older children back into the property unharmed but unfortunately she's been hurt herself with minor injuries while she's been trying to protect the two-year-old.
'She (the girl) has got extensive injuries to her face, to her neck and to her body and only time will tell if she fully recovers from that attack.
'We know one, if not more, of these dogs was involved in the attack but we need to establish what went on. If the aunt of that two-year-old child hadn't intervened we could have been looking at a much more serious situation in this case.'
He described the victim's family as traumatized and appealed to the public to report any worries about dangerous dogs or irresponsible owners to police.
He added: 'If you do insist on having a dog, you should put a muzzle on it if you have it in public.'
Neighbors described the dogs as 'XXL American Bull Dogs' which were being bred for sale.
The neighbor lived at the address with his partner and three children.
Emergency services were first called to the house at about 3.40pm on Sunday after reports a child had been bitten by a dog and a woman had also been injured.
One neighbor described hearing the girl scream as the dog attacked her.
Another said she saw the aunt dash from the house carrying the girl screaming: 'The dog's got the baby! The dog's got the baby!'
The neighbour added: 'I can't even actually think about it now,' and was too upset to speak further.
The girl was treated at the scene by paramedics before being taken by air ambulance to hospital.
Her condition is described as serious but not life-threatening.
The aunt who rescued the child from the dogs was taken to the Royal Liverpool University Hospital where she received treatment for minor injuries and was later released from hospital.
Police seized five dogs and six puppies from the home of the man who was arrested.
Neighbours said the dogs were kept in cages at the back of the house.
Chief Inspector Dave Westby said: 'This was a horrific attack which has resulted in a two-year-old girl suffering extensive injuries to her head and body.
'The investigation is in its early stages, but it is believed that the child was playing in the back garden of a relative's address with two other children, aged four and six years, when a number of dogs from a nearby house managed to get in to the garden.
'At this stage it is believed that the little girl was attacked by more than one dog, and officers are trying to establish how many dogs were involved in the incident.
'Fortunately, a relative who was in the house was able to rescue the child from the dogs.
'I want to reassure people that the little girl is now getting the best possible care and treatment for her injuries at Alder Hey Children's Hospital.
'An extensive investigation is under way to establish exactly what has happened and to determine how many dogs were involved in the incident and the breed of dogs involved.
'I would appeal to anyone who was in the area at the time of the incident, who may have information which could help us with our investigation, to come forward as soon as possible.'
A large police presence remained at the scene on Monday, with forensic officers in white boiler suits seen going to and from the house.
According to locals, the youngster is well known and is 'very smiley, adorable'.
Chief Insp Westby added: 'I would appeal to anyone who was in the area at the time, who may have information which could help us with our investigation, to come forward as soon as possible.'
Last month, police shot and killed two American bulldogs after they ran amok in Bolton, biting one woman on the hand and another on the leg.