Maria and William Henniker-Gotley, aged 51 and 55 and from south London, died after the 6.2 magnitude quake struck in the early hours of Wednesday morning.
Marcos Burnett, 14, was also killed.
A statement from their families said: "It is with sadness that we can confirm the deaths of Maria, 51, and Will, 55, Henniker-Gotley and Marcos Burnett, 14, in the earthquake in Amatrice, Italy on 24 July.
"Their families have paid tribute to the tireless work of the Italian rescue workers and hospital staff and expressed their gratitude for the love and support they have received from the Italian people. Their thoughts and prayers are with all those affected by the earthquake."
The earthquake levelled three small towns and has left at least 250 people dead.
A state of emergency has been declared in the areas affected and aftershocks have continued to strike, including one of a preliminary magnitude of 4.7 on Friday morning.
It is believed Mr and Mrs Henniker-Gotley owned a property in Sommati, a village about 1.3 miles (2km) from Amatrice.
Their two children, believed to be aged 12 and 14, survived but their condition is unknown.
A neighbour, who did not want to be named, said: "It's terrible news, so awful. I knew them all very well.
"They were lovely. They were a lovely family. It's very hard to take in.
"They were very warm and friendly, extremely good neighbours. It's just so awful to think of their children."
She added: "I think Maria's father came from the village and was possibly born there. When he was ill - he has since died - they bought a house there and they go out every summer."
Another neighbour, who also did not want to be named, said: "They were just absolutely lovely people. He was an entrepreneur and she was finance director for Children & The Arts."
Marcos and his family were staying with the Henniker-Gotleys.
His parents, Anne-Louise and Simon Burnett, were both taken to hospital and their daughter also survived. Her condition is unknown.
The mother and father were initially taken to separate hospitals 40 miles (60km) from each other, where she was treated for facial fractures and he was being treated for a broken leg.
Rieti Hospital director Pasquale Carducci said: "The British woman was brought here by rescue workers on Wednesday while her husband was taken to L'Aquila.
"When we discovered he was there, we decided they would be happier together, so we decided to reunite them.
"Since the man was less badly hurt, it was easier to bring him to her. We hope that they can be a support to each other."
The latest aftershock hit the region at 6.28am local time on Friday. The US Geological Survey said it had a preliminary magnitude of 4.7.
Italy's national geological institute put the magnitude at 4.8. It was preceded by more than a dozen weaker aftershocks overnight and followed by another nine in the subsequent hour.
The quake zone has experienced more than 500 aftershocks, some measuring 5.1, in the two days since the original pre-dawn quake on Wednesday.
Foreign Secretary Boris Johnson said on Thursday that a number of Britons had been "affected" by the earthquake.
He said extra staff had been sent to the region to help provide support to Britons, while the Government has offered "any assistance that we can" to the Italian authorities.
He said: "My deepest sympathies are with the Italian people and everyone affected by the terrible earthquake that struck central Italy.
"The British Government has offered any assistance that we can to help with the recovery effort and I have spoken with Italian Foreign Minister Paolo Gentiloni to express my condolences personally.
"As the scale of the disaster has become clearer, we now know that a number of British nationals have been affected.
"British embassy staff are in the region providing consular support, and we have deployed additional staff to support this effort."
Firefighters and rescue crews using sniffer dogs have been working in teams around the hardest-hit areas of the country.
"We will work relentlessly until the last person is found, and make sure no-one is trapped," said Lorenzo Botti, a rescue team spokesman.
A Foreign Office spokesman said: "We are providing support to the families of Marcos Burnett and Will and Maria Henniker-Gotley following their tragic deaths in the earthquake in Italy. Our thoughts are with them at this incredibly difficult time.
"British Embassy staff will continue working with local authorities regarding any further British nationals that may require our assistance."