Mother-of-three Elayne Stanley, 44, was mauled at the house in Widnes on Tuesday evening.
Neighbours said they heard screams from the home in Graham Road before police arrived to find Ms Stanley seriously injured.
Cheshire Police said one of the dogs had to be destroyed while the other had been captured and taken to a secure kennel.
No arrests have been made.
Neighbours said that the dogs turned on Ms Stanley, who was the mother of three daughters.
The dogs were Mastiff-types called Billy and DJ.
One local resident said: ‘I was sat upstairs and I just heard a girl shouting “DJ”. I heard the girl screaming “I can’t get to her” and the next thing someone was kicking the door in.
‘I know they were American bulldog type dogs. She was only a little woman, she didn’t really stand a chance.
‘They always seemed like they were nice enough dogs, they were never out of control. You don’t know what’s provoked it. I’ve heard people saying there was an argument but you just don’t know.
‘The police must have shot them because I heard the shots, it sent our two dogs crazy.’
Another neighbour recalled how local residents went to her aid.
Bev Hall, 39, who lives opposite and has been friends with Ms Stanley for 22 years, told the Mail Online: ‘We both dropped everything and ran over bare-footed.
‘The living room door was closed and Elayne was behind it so we couldn’t get in.
‘I could hear a dog growling and scratching, we threw all sorts to and banged on the windows to try and distract the dogs.
‘Then the police were called, my partner and a couple of the neighbours started throwing bricks at the dogs from the side door.
‘Once the dogs were in the back garden my partner locked them out.
‘By the time the paramedics came there was nothing they could do.’
The girl dog Billy was tranquilised and taken away but DJ was put down at the scene.
In statement Cheshire Police said: ‘At around 5.15pm on Tuesday 24 September police received reports that a 44-year-old woman had been attacked by two dogs at an address on Graham Road in Widnes.
‘Officers attended the property and discovered that the woman was in a serious condition. Sadly, despite the best efforts of all those involved, the woman died at the scene. Her next of kin have been informed and are being supported by officers.
‘Following the attack, repeated attempts were made by officers to safely secure the two dogs in order to remove them from the address.
‘One was safely detained, however officers were unable to secure the second dog. Attempts were made to tranquilise the second dog but this was unsuccessful so, in the interests of public safety, the dog was destroyed. The other dog remains in a secure kennel.’
Detective Inspector Ian Whiley said: ‘We understand that people in the local community will be concerned when they hear about what has happened.
‘But I would like to reassure residents that we are doing all that we can to establish the full circumstances of the incident.
‘However, at this stage, it is believed that the dogs were known to the woman and were living at the address. This has been an extremely distressing incident and our thoughts are with the woman’s family at this difficult time.’