Jamie Barrow, 31, had admitted their manslaughter at Nottingham Crown Court but denied three counts of murder.
On Tuesday a jury found him guilty of the more serious charges.
The trial heard Barrow had poured petrol through the letterbox of the family's Fairisle Close flat in the early hours of 20 November and set it alight.
Jurors were told he was unhappy about bags of rubbish being left in an alleyway behind where he and the victims lived but police said no clear motive had been established.
Prosecutors said Barrow knew the flat's front door was the only way in and out when he set the fire.
He had claimed he thought the property was empty but the court was told he did nothing when he heard screams.
Ms Hydara and her daughters died from smoke inhalation.
Prosecutors said Barrow had lit the fire using tissue paper and petrol from his motorbike.
They said it would have been clear the family were inside because a pram was left outside the door and there was light coming from the hallway.
After setting the fire Barrow was seen on CCTV walking away from the burning flat with his dog while smoking a cigarette, police said.
Emergency services attended the scene and police said Barrow later returned and asked officers "how bad" the fire was.
Barrow, who admitted drinking "seven or eight" pints of lager before starting the fire, had given evidence to the police afterwards when detectives were treating the incident as a hate crime.
He later admitted his involvement to them.
In court he claimed he had been suffering from a "very, very low mood" and was "wallowing in self-pity" before starting the fire, caused partially by his emotionally unstable personality disorder.
He said he did not expect the blaze to take hold as rapidly as it did and was driven to admit what he had done to officers due to "an immense amount of guilt".
In addition to murder, Barrow was also convicted of one count of arson being reckless as to whether life was in danger and is due to be sentenced at the same court on Friday.
Some members of the victims' family, to whom he apologised while giving evidence, wept after the verdicts were delivered.
After Barrow's conviction, relatives of Ms Hydara and her children released a statement describing their pain and grief.
They said: "Words cannot quantify how much our family have suffered because of the horrific actions of one man.
"Neither can we quantify the emotional, psychological, physiological and financial impact of the crime Jamie Barrow committed against Fatoumatta, Fatimah and Naeemah.
"His actions were utterly heartless and cruel - and have caused a multigenerational trauma that we will never understand.
"Fatoumatta was a caring daughter, wife, sister, mother and friend. If love and compassion could make a person immortal, she would have lived forever.
"She had a pure heart and was greatly loved for her personality and qualities.
"She was the most incredible mother to Fatimah and Naeemah, two angels who deserved a beautiful childhood and a full life.
"Nottingham and the rest of the world have been denied potential future teachers, civil servants, doctors - who knows what they could have been?
"They lived a short but meaningful life, such was the joy and happiness they brought to us all."
Ms Hydara's family thanked the Gambian community in the UK and internationally for the support it had offered them since the fatal fire.
They also thanked Nottinghamshire Police, the Crown Prosecution Service, and the jurors.
Before they died Ms Hydara and her children had been planning to move to the US to be with her husband Aboubacarr Drammeh.
Det Insp Kaz Smithson, who led the investigation, said: "Jamie Barrow committed the most despicable crime anyone could ever commit.
"He destroyed a whole family and took away their dreams of a happy life together in America.
"Today, justice has been served for Fatoumatta, Fatimah and Naeemah and their family, all of whom have carried themselves with incredible dignity since the night of this truly awful crime.
"Barrow denied the killings were deliberate but, thankfully, my investigative team was able to provide overwhelming evidence that this tragic event was indeed murder.
"We saw through his lies and, thankfully, so did the jury."
After the hearing Nottinghamshire Police said Barrow's motive for starting the fire might never be known but jurors heard one theory was that he wanted to rehoused by local authorities.
Ch Insp Karl Thomas said: "I acknowledge there are many members of the community who believe these murders were a hate crime.
"It's important to say that, following a very detailed and thorough investigation by a large team of detectives, the investigation team left no stone unturned to investigate the circumstances and presented the evidence to the jury to reach these verdicts."
Source: BBC News
