The UK government has already offered to help with the recovery effort, as about 5,000 rescue workers are combing the rubble for survivors.
Mr Johnson 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."
The rescue effort has been hampered by hundreds of aftershocks, including a magnitude 4.3 strong tremor that hit this afternoon.
Rescue workers and firefighters are using heavy machinery, sniffer dogs, and their bare hands to comb the wreckage for survivors.
Lorenzo Botti, a rescue team spokesman said: "We will work relentlessly until the last person is found, and make sure no one is trapped."