The woman was travelling in the economy section when she suddenly went into cardiac arrest in front of other passengers including children.
The London Ambulance Service were called to Heathrow Airport Terminal 2 to board United Airlines flight UA880 from the US at 7.07am.
A United Airlines spokesman said: “A customer onboard United flight 880 today, from Houston to London Heathrow, experienced a medical emergency onboard.
“Medical personnel met the aircraft on arrival at London Heathrow. We extend our deepest condolences to the customer’s family and loved ones.”
Scotland Yard said: “Police were called following reports that a 51-year-old woman had died on a flight arriving into Terminal 2 at Heathrow from the United States. Officers attended.
“The woman’s death was unexpected, it has been investigated and is not suspicious.
“Her next of kin are aware and a file will be prepared for the coroner.”
A London Ambulance Service spokesperson said: “We were called at 6.33am today (5 October) to reports of a passenger having suffered a cardiac arrest onboard a flight due to arrive at Heathrow Airport Terminal 2.
“We sent two cycle paramedics and an incident response officer. Sadly, a woman was pronounced dead at the scene.”