Fourteen firefighters battled the blaze which broke out at a large semi-detached home in Battle Road at about 8.30am today (August 19).
East Sussex Fire and Rescue Service said a man and a dog were rescued from the first floor of the property.
An elderly woman and another dog were in the ground floor of the home and died at the scene, the spokesman added.
Battle Road has been closed in both directions from Upper Glen Road to Telford Road due to the incident.
Six fire engines were called and crews used 14 breathing apparatus, two foam jets, two hose reels and a water jet to fight the flames.
The fire has been extinguished and firefighters remain at the scene.
Assistant Chief Fire Officer Mark Andrews praised members of the public who assisted crews in accessing the building and also highlighted the courageous operational response from both Sussex Fire Control and firefighters.
An investigation has been launched into the cause of the fire.