SMS Scharnhorst was the flagship of German Vice-Admiral Maximilian Graf von Spee's East Asia Squadron.
It was sunk on 8 December 1914 with more than 800 men on board, including Vice-Adm von Spee himself.
The leader of the search for the wreckage said the moment of discovery was "extraordinary".
'Poignant moment'
"We are often chasing shadows on the seabed, but when the Scharnhorst first appeared in the data flow, there was no doubt that this was one of the German fleet," Mensun Bound said of the moment of discovery.SMS Scharnhorst was part of the East Asia Squadron, the Imperial German Navy's cruiser squadron which operated mainly in the Pacific Ocean until the outbreak of World War One in 1914.
The armoured cruiser played a key role in Battle of Coronel, fought between the British Royal Navy and Germany's Imperial Navy off the coast of Chile
From victory to defeat in five weeks
It was Britain's first naval defeat of World War One and it was a devastating one. The Germans sank two of the four British ships with the loss of more than 1,600 lives. Not a single German sailor died.The defeat at Coronel sent shock waves through the British empire and beyond.
But the British response was not long in coming.
The Royal Navy despatched ships from the North Sea down to the South Atlantic and confronted the Germans at the Falkland Islands five weeks later.
The British squadron pursued and engaged the German squadron. HMS Invincible and HMS Inflexible inflicted substantial damage on the SMS Scharnhorst, causing it to sink with all 860 people on board. The Royal Navy then gave pursuit to the remaining German ships.
Vice-Adm von Spee's two sons also died, Heinrich on board the SMS Gneisenau and Otto aboard the light cruiser SMS Leipzig. In total, 2,200 German sailors died in the battle.
The head of the von Spee family said that the discovery of the wreck was "bittersweet". "We take comfort from the knowledge that the final resting place of so many has been found, and can now be preserved, whilst also being reminded of the huge waste of life," Wilhelm Graf von Spee said.
"As a family we lost a father and his two sons on one day. Like the thousands of other families who suffered unimaginable loss during the First World War, we remember them and must ensure that their sacrifice was not in vain."
Vice-Adm von Spee was hailed as a hero in Germany for not surrendering and in 1934 a new heavy cruiser was named after him.
The Battle of the Falkland Islands had a lasting effect on World War One because as a result the East Asia Squadron, Germany's only permanent overseas naval formation, effectively ceased to exist and could no longer engage in commerce raiding.
SMS Scharnhorst was named after the chief of the Prussian general staff during the Napoleonic Wars
