The earl - who was murdered nine days ago by the IRA during a fishing trip in County Sligo - had planned much of the funeral himself.
Members of Britain's armed forces were joined by representatives of Burma, India, the United States, France and Canada in escorting the naval gun carriage carrying his body.
The procession from Wellington barracks, near Buckingham Palace, to Westminster Abbey was accompanied by the sound of bells and the solemn brass of Royal Marine bands.
The cocked hat of an admiral of the fleet, his sword of honour and his gold stick were laid on top of the earl's coffin.
Lord Mountbatten's horse, Dolly, was led near the head of the parade with the admiral's boots reversed in the stirrups.
'So rare a person'
Thousands lined the route of the procession and the memorial service at Westminster Abbey was attended by royalty, leaders and politicians from all over the world.
The Archbishop of Canterbury praised the earl for his "lifelong devotion to the Royal Navy" and for being "so rare a person".
After the public ceremony the coffin was taken to Romsey Abbey near the Mountbatten's family home in Hampshire and buried at a private service.