The “world’s most challenging shipwreck search” for one of the greatest legends of exploration history, Sir Ernest Shackleton’s Endurance, lost more than a century ago in the icy waters of Antarctica, has succeeded.

The wreck has been found, 3,008 metres below the surface of what Shackleton described as “the worst portion of the worst sea in the world”. It was discovered on Saturday, the 100th anniversary of Shackleton’s funeral, the Falklands Maritime Heritage Trust said.

The Endurance22 expedition, which set off from Cape Town a month ago, had “reached its goal”, said Dr John Shears, the veteran geographer who led the expedition. “We have made polar history with the discovery of Endurance, and successfully completed the world’s most challenging shipwreck search.”

He hoped people would be inspired by “what human beings can achieve and the obstacles they can overcome when they work together”.

Arcing across the submerged ship’s wooden stern is its famous name, preserved by the freezing waters and the absence of wood-eating organisms.

The Endurance was found off the coast of Antarctica, approximately four miles south of the position originally recorded by its captain, Frank Worsley. It has not been seen since it was crushed by ice and sank in the Weddell Sea in November 1915.

Mensun Bound, the expedition’s director of exploration, said footage showed the 144ft ship to be intact.

“We are overwhelmed by our good fortune in having located and captured images of Endurance,” he said.

“This is by far the finest wooden shipwreck I have ever seen. It is upright, well proud of the seabed, intact, and in a brilliant state of preservation … This is a milestone in polar history.”

Dan Snow, the historian and broadcaster who is part of the expedition, said the mood on board ship was jubilant, and the team was now heading home.

He tweeted: “The wreck is coherent, in an astonishing state of preservation. The Antarctic seabed does not have any wood-eating micro-organisms, the water has the clarity of distilled water. We were able to film the wreck in super-high definition. The results are magical Endurance22.”

He added: “Nothing was touched on the wreck. Nothing retrieved. It was surveyed using the latest tools and its position confirmed. It is protected by the Antarctic Treaty. Nor did we wish to tamper with it.”

The site of Endurance was declared a historic monument under the terms of the 1959 Antarctic Treaty.

An expedition team of 64 people, plus a crew of 46, were on board the expedition ship, the SA Agulhas II. The $10m mission was financed by an anonymous donor. A previous attempt to find the Endurance three years ago ended in failure.

Shackleton famously lost his ship but saved his crew. He set sail from South Georgia in December 1914 with 27 men, heading for Vahsel Bay on the eastern side of the Weddell Sea. The plan was to cross the vast Antarctic ice sheet to the south pole, and then keep going, to the Ross Sea on the other side of the continent.

But two days after leaving South Georgia, the Endurance encountered polar pack ice. By early January, the ship became stuck and eventually the crew decamped to the ice, taking the ship’s stores of food and other provisions, and three open lifeboats. On 21 November 1915, the Endurance finally sank, with Captain Worsley recording its position.

Shackleton and his party continued camping on the ice floes for another five months, before sailing in the lifeboats to Elephant Island. From there, in freezing temperatures and rough seas, Shackleton, Worsley and four others sailed 800 miles to South Georgia. They organised the rescue of the rest of the crew, who were picked up alive within months.

As well as finding Shackleton’s ship, the Endurance22 expedition had undertaken important scientific research in a part of the world that directly affects the global climate and environment, Shears said.

“We have also conducted an unprecedented educational outreach programme, with live broadcasting from on board, allowing new generations from around the world to engage with Endurance22 and become inspired by the amazing stories of polar exploration, and what human beings can achieve and the obstacles they can overcome when they work together.”