Jatindra Lad, 49, his wife, Duksha Lad, 44, and their daughters, Trisha, 19, and Nisha, 17, were found dead at their home in Clayton last night.
West Yorkshire Police have launched a murder investigation but said they are not looking for anybody else in relation to the deaths.
Officers were called to the house in Blackberry Way at 8:31pm last night after they were contacted by a neighbour who was concerned that they had not seen the family for some time.
Police said early indications suggest the bodies may have been in the property “for some time”.
Post-mortems will now be carried out to establish the cause of the deaths, police said.
Detective Superintendent Simon Atkinson of West Yorkshire Police said: “This is clearly a significant incident and our investigation will be thorough as we piece together the events that have led to the deaths of a local family.”
“The investigation is at an early stage and while I do not want to speculate around the circumstances leading to the deaths, I am happy to confirm that we are not looking for anyone else in connection with this incident,” he said.
Damien Miller, Superintendent Operations of Bradford District, who leads neighbourhood policing across the Bradford District, said: “Clayton is a close knit community and I understand that local people will be understandably upset by what has taken place and I would like to reassure people there is no wider danger to members of the public.”
“Additional neighbourhood officers are in the area speaking to people and offering reassurance,” he said.
The family had lived in the “peaceful” village for at least 20 years.
A white car was parked on the driveway of the detached two-storey house that was sealed off with police tape for a forensic investigation.
Lorna Leeming, who sits on Clayton parish council, said: “It’s a very quiet and peaceful village and a good community. I don’t know what has happened or what has gone on.”
Sehaj Singh, 19, said he had known the older daughter for eight years and added she was in her second year at Leeds University.
Describing her as a quiet girl, Singh was quoted as saying: “She was really nice. She was just one of those people who got on with things.”
Jessica Garside, 18, who went to nearby Thornton grammar school with the older girl, said of her friend: “She was a lovely person. Never said anything bad about anybody.”