The group said they came across the wreckage at an altitude of about 10,500ft about 215 miles south of Santiago, the capital.
The incident was one of the world’s major air disasters involving football teams. Also among the fatalities were three referees.
The disappearance of the Douglas DC-3 carrying members of the top-division Chilean team Green Cross on 3 April, 1961 was one of the great unsolved mysteries in the South American country and at the time stunned the sporting world.
The club had played an away match in Osorno in the Copa de Chile and was returning to Santiago.
The team and staff were spread over two flights. One of the planes reached the Chilean capital and the other vanished.
Rescuers spent fruitless weeks searching for the plane and symbolic funerals for the missing players drew huge crowds in Chile.
Expedition member Leonardo Albornoz described the moment the team discovered the wreckage.
“It was a breathtaking moment and we felt all kinds of sensations. One could feel the energy of the place and breathe the pain,” he said.
“The plane is more 10,000ft above sea level. A large part of the fuselage is still intact and a lot of material including human bones are scattered around the wreck.”
Video footage shot by the mountaineers show the twisted wreckage of the aircraft buried in stones.
The mountaineers said they could see a good part of the fuselage without needing to dig it out and found scattered debris and bones.
The location of the wreckage was not where official publications indicated it should be, but Mr Albornoz said that are keeping the exact site secret to prevent looting.
He said: “We don’t want this place to be defiled and the remains taken as trophies. You have to remember people died here and their families deserve respect.”
The Chilean club had played a cup match against Osorno Seleccion on 1 April, 1961.
It ended in a 1-1 draw and the club’s team and staff flew back to Santiago.
It was reported that most of the first team players had elected to fly on the fateful plane because it was more direct, and the alternative flight was scheduled to make several stops on the way back to Santiago.
Despite having lost almost the entire first team in the crash, the club still played the second leg of the cup tie, losing 0-1 and being knocked out of the cup.
It went on to finish 12th out 14 clubs in the league and was relegated a season later.
However, the team managed to regain its position in the top league the following season, and Green Cross played in Chile’s first division until the club was dissolved in 1965.
The tragedy has echoes of a widely publicised disaster that followed in 1972, when a Uruguayan aircraft carrying a rugby team and their friends went down in the Andes in Argentina, near the border with Chile.
Of the 45 on board the flight, only 16 survived the harsh conditions, and were forced to resort to eating the dead in order to stay alive.
The plane’s survivors became the inspiration for numerous documentaries, movies and books, most notably the 1993 film Alive, which was based on a book by the same name.