Jordan Green, 12, and his nine-year-old brother Tyler were killed along with their mother Josie Leighton, 32, and her friend Claire James, 27, in the blaze at a house in North Wingfield, near Chesterfield, on Wednesday.
Ms James’s seven-year-old daughter was taken to hospital after escaping to the back garden and has since been discharged.
In a statement, Ms Leighton’s mother Lynn said: “Josie was a lovely, loving daughter who had lots of friends.
“Tyler was always happy. He loved life, he loved school and was always full of beans. Jordan was a real character. He loved his family, specially his grandma and always had lots of friends.
“They will all be greatly missed. We are devastated by what has happened.”
The fire brigade were on the scene within eight minutes after a neighbour raised the alarm at 4.58am.
Firefighters tackled “arduous conditions” inside in an attempt to rescue the other occupants.
Ms James and Ms Leighton were pronounced dead at the scene while young Tyler and his brother were pronounced dead later at Chesterfield and District Royal Hospital.
Ms James’s family said: “We are devastated by our loss and want to be left alone to grieve,” adding that supporting her daughter was their main priority. Derbyshire Police said the fire’s cause was not thought to be suspicious.