The man, believed to be in his late 50s, died at Thorpeness in Suffolk on Saturday afternoon. An elderly woman suffered minor injuries but was not taken to hospital.
It is believed the man was walking his dog at the base of the cliff when it collapsed on top of him. The dog is safe and with the man's family.
Suffolk Police said that they were treating the death as "non-suspicious".
The coastguard said it received multiple 999 calls from members of the public telling them a man was trapped.
Police, fire, ambulance and coastguard crews all took part in the rescue effort.
Erosion has been an issue on this stretch of coast for a number of years.
Large wire baskets full of stones and rocks, called gabions, were installed at Thorpeness in 2010 to bolster sea defences after storms left the cliffs exposed.
People have been urged to be "mindful" when walking on the coast, particularly while walking at the bases of cliffs.
A section of beach where a man died in a cliff collapse remains cordoned off.