Harry and the 12 servicemen and women reached the globe's most southerly point at 1200 GMT following a 200-mile journey across Antarctica, organisers Walking With The Wounded said.
"It's an amazing feeling, it really is," Harry, 29, said in a statement issued by Walking With the Wounded after the group reached the pole.
The fourth-in-line to the throne added: "What an amazing journey for every single one of them. I'm so proud, I'm so chuffed and I'm so privileged to be here with all these guys and girls.
"I think we'll be having a few whiskies tonight and then everyone's looking forward to getting home."
The expedition was initially conceived as a race but it was abandoned due to concerns about the safety of the participants, some of whom lost limbs fighting in Afghanistan and Iraq.
The teams decided to continue their trek, however, dragging 70-kilogramme sleds through the bitter cold and high winds.
Harry, who serves as an army helicopter pilot, joked earlier this week about the expected arrival date of Friday 13th, which he said was "unlucky for some, lucky for us".
The veterans have endured temperatures as low as minus 35 degrees Celsius (minus 31 degrees Fahrenheit) and wind speeds of around 50 miles per hour.
The trek has been organised by Walking With The Wounded, a charity which raises funds to retrain injured troops and help them find new careers outside the military.
Harry joined the charity for part of a trek to the North Pole in 2011, but had to come home early to be best man at his brother Prince William's wedding to Kate Middleton.
While Queen Elizabeth's grandson is the first royal to reach the South Pole, Britain's monarchy has a number of links to the frozen continent.
Prince Philip crossed the Antarctic circle in 1957 on board the now-retired royal yacht Britannia while visiting a memorial cross to polar explorer Ernest Shackleton on the remote Atlantic island of South Georgia.
Harry's aunt Princess Anne has twice visited Antarctica, most recently in 2007.
The queen herself had a huge chunk of Antarctica named after her in a gift from the government to mark her diamond jubilee in 2012.
Queen Elizabeth Land is around 169,000 square miles in size, making up just under a third of British Antarctic Territory.
