Harriet Forster died after suffering head injuries when a section of cliff fell on a beach in Staithes on Wednesday.
At the time, she was visiting the village with her family from their home in Oxford.
In a statement issued by North Yorkshire Police, the girl’s family said: “We cannot comprehend the enormity of this tragedy. Harriet was the light of our lives.
“We ask that you give us time as a family to support each other through our indescribable pain. Thank you.”
Emergency services were called to Seaton Garth in Staithes at 4.45pm after reports the girl had been injured.
Despite the efforts of the emergency services, she died at the scene.
In a statement on the day of the incident, it said: “Numerous calls were made to the emergency services after a section of the cliff fell.
“Thank you to all the emergency services, coastguard teams and personnel for their very best efforts.”
Officers said they are compiling a report about the circumstances of the death on behalf of the coroner.