Merseyside Police identified them as Elisha Brabin, 36, Leo Brabin, 16, Ellis Brabin, eight, and seven-year-old Prudence Brabin.
The family said they have suffered an “unimaginable” loss.
In a tribute issued through police, relatives of the family said: “Our whole family is devastated by the loss of Elisha, Leo, Ellis and Prudence.
“Elisha was our beloved daughter, wife, mother, sister, auntie, niece and cousin. She was a devoted and loving mother who lived for her children. They were her whole world, and she meant everything to us.
“Our beautiful babies, Leo, Ellis and Prudence, were loved beyond measure and brought so much joy, happiness and love to our family. They filled our lives with laughter and precious memories that we will cherish forever.
“The tragic loss of Elisha and our three precious children has left us heartbroken. They have all been taken from us far too soon. The loss we are experiencing is unimaginable, and the impact on our family will be felt forever.”
One person found outside the house was also taken to hospital with burns.
Firefighters were called to the property in Stone Square at 3.38am on Tuesday.
Chief fire officer Nick Searle, of the Merseyside Fire and Rescue Service, said it was an “intense fire which spread very rapidly”.
Six engines were on scene at the height of the blaze and eight firefighters entered the house, said a spokesperson.
“I heard shouting in the early hours but I just thought someone was having an argument,” said a neighbour. “Then I came downstairs and saw all the fire engines.”
Police and firefighters are jointly investigating the cause of the blaze.
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