Former Test captain Ian Chappell had led a push for the team to be officially recognised and made a formal presentation during the tea break on the second day of the second Test between Australia and Pakistan on Monday.
Chappell, who played 75 Tests from 1964-65 to 1979-80 and is now a commentator, told the crowd at Melbourne Cricket Ground this was a special and long-awaited occasion.
"I'm delighted this recognition ceremony is going on," the 61-year-old Chappell said.
CA said in a statement: "The 14-member touring party will be assigned individual player numbers.
"This follows the tradition of presenting player numbers to Australian debutants in Test and one-day international cricket," the statement added.
Australia's first female Aboriginal to be selected for a national side, Faith Thomas, and Len Clarke, a descendant of 1868
CA chairman Bob Merriman said: "The 1868 Aboriginal tour of England marks an important event in Australia's sporting and cricket history as the first cricket team to tour England.
"The courage and optimism of the 1868 team to undertake and participate in such a lengthy tour, under the conditions of that era, is an inspiring journey."
The 1868 team included 13 Australian Aborigines and English captain-coach Charles Lawrence. It was the first Australia team to tour England.
The team's five-month tour included 47 games, winning 14, losing 14 and drawing 19 matches.
The first official Australia v England Ashes Test was played in Melbourne in March 1877.