Before taking the final transatlantic flight, Captain Mike Bannister said: "Concorde was born from dreams, built with vision, and operated with vision."
Joan Collins and husband Percy Gibson were among the VIPs on board the historic flight.
Before leaving New York, the plane was showered in red, white and blue jets of water.
Flight BA002 left New York's JFK airport at 1235 BST with 100 celebrities on board, on a sunny autumnal day.
The Anglo-French project was conceived in 1962 and 31 years later, it took its final journey into Heathrow.
The Gallic contribution was not forgotten by some, although Air France finished its Concorde in May.
Hundreds of onlookers arrived early in the day and some set up informal vantage points around the Heathrow perimeter fence.
Competition winners enjoyed the other two last Concorde flights, one from Edinbugh and another which took in the Atlantic.
The famous plane was retired because it was deemed unprofitable by British Airways and Air France.