The man, in his 60s, was a passenger in the vehicle which collided with a building in Mill Street in Leominster at around 6.40am, West Mercia Police said.
West Midlands Ambulance Service (WMAS) said two others, the driver and another passenger, were seriously injured and taken to hospital.
A multi-agency response has been set up, co-ordinated through the Herefordshire Tactical Co-ordination Group (TCG), police said.
Speaking on behalf of the TCG, Superintendent Helen Wain said: "Shortly after 6.40am this morning, emergency services responded to a report a bin lorry had collided with a building in Mill Street in Leominster.
"Three people were in the vehicle at the time of the collision and it has now been confirmed that sadly a man in his 60s, who was a passenger, was pronounced dead at the scene.
"The driver and a second passenger were treated at the scene by paramedics and taken to hospital for treatment."
The building, which was initially thought to have been a house, was empty at the time and no-one else was injured.
Ms Wain added: "On behalf of all agencies, our thoughts and condolences are with those involved and families affected by the incident.
"A cordon remains in place while the fire service and local authorities continue to work to make the building safe. Roads surrounding the building are closed and are expected to remain closed for some time.
"We ask you to avoid Mill Street and the surrounding area and find an alternative route."
WMAS said it received multiple 999 calls at around 6.45am reporting a refuse lorry had collided with a property and two ambulances, two paramedic officers, a Merit trauma doctor with a critical care paramedic, the Hazardous Area Response Team (Hart), two Mercia Accident Rescue Service (Mars) Basics doctors, the Midlands Air Ambulances from Strensham and Cosford and a Critical Care Car from Midlands Air Ambulance responded to the scene.
A spokesman said: "Ambulance staff arrived on scene to find a significant RTC where three occupants were trapped in a bin lorry which had collided with a (building).
"Due to structural damage to the (property), all three emergency service colleagues worked rapidly together to safely extricate the three patients.
"Sadly, one male passenger was confirmed deceased on scene.
"The driver, a man, received trauma care by ambulance staff for serious injuries before being airlifted to Queen Elizabeth Hospital Birmingham for further emergency care.
"A second male passenger also received trauma care for serious injuries by WMAS before being airlifted to the same hospital for further trauma care."
Herefordshire Council thanked the emergency services for their "swift response", saying: "We are working with our partners to assess the situation. We are asking people to avoid the area to allow the emergency services to safely carry out their work.
"Our thoughts are with those involved in the incident and their families. We would like to thank the emergency services for their swift response. Further updates will be issued when more facts are known."
