The bodies of Jitendra Lad, 49, his wife, Daksha Lad, 44, and their daughters, Trisha, 19, and Nisha, 16, were found at their detached home in Clayton, last night.
Police launched a murder investigation but said they are not looking for anyone else in relation the deaths.
They said early indications suggest the bodies may have been in the house “for some time” but have given no details of the circumstances in which they were found.
Tributes were paid to the “lovely” family.
Both girls are thought to have attended Thornton Grammar School in the city and Trisha was in the second year of a biochemistry degree at Leeds University.
Jessica Garside, a friend of the older sister, said: “She was so lovely. She always had a bright smile on her face.
“She was always happy.”
She said: “Even when I saw her round school she would always smile and say ‘hello’ and check I’m all right. I think that was the general gist of the family.”
Melissa Taylor, president of the Faculty of Biological Sciences Society at the university, said on Twitter: “Heartbreaking to hear about the death of Trisha Lad, such a lovely, well-liked person. Rest in Peace.”
Steph Mapplebeck said: “Trisha Lad was one of the sweetest and kindest people I have met whilst studying at Leeds. What a heartbreaking loss. Rest in peace.”
A spokesman for the University of Leeds said: “This is dreadful and shocking news and our thoughts are with Trisha’s friends and loved ones.”
Chris Sampson, headteacher of Thornton Grammar, said: “We are deeply shocked and saddened by these tragic deaths. Our thoughts are with the family’s relatives and friends. We will be helping the police with their inquiry in any way we can.”
Mr and Mrs Lad both worked as clerical officers at Bradford council, where colleagues were said to be “very upset”.
David Green, leader of the local authority, said: “Local people are shocked and saddened by the news of this terrible event and our sympathy goes out to the wider family, friends and neighbours of this family.
“The husband and wife of the family... both worked for Bradford Council and councillors and employees are very upset after hearing the dreadful news of their deaths.”
Neighbour Barry Hawkins said: “I used to say hello to the mum and dad and I used to see the daughter go to school. I’ve seen them grow up.
“I’ve delivered papers up here for 20 years so I know everybody.
“They were a lovely couple and the kids were lovely. Well mannered. They were well respected.
“I’ve know them for 10 years. It’s bad but it’ll pull us all together.”
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 recently.
Detective Superintendent Simon Atkinson 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.
“We are now undertaking forensic inquiries to establish how these people have died.
“We are clearly keeping an open mind but from what we know at the moment we are not looking for anybody else.
“It is an extremely distressing time for the family and friends. We are trying to get as many answers as to what has happened in the property.”
The quiet cul-de-sac was cordoned off today but police were letting groups of tearful teenagers up to the modern house.
A number of uniformed officers and forensic scientists could be seen working in the front garden and around a white hatchback car in the drive.
Superintendent Damien Miller 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.”
Lorna Leeming, who sits on Clayton Parish Council, said: “It’s a very quiet and peaceful village and a good community.”