Jackson, 31, led the Opals to silver in Beijing four years ago and is competing in her fourth Games. She will be the first Australian woman in 20 years to lead out her country at a Summer Olympics.
"Why me?" was her immediate response. "There are other candidates better than me."
Chef de Mission Nick Green, announcing his decision, said Jackson was an "unassuming athlete with wonderful leadership qualities on and off the court".
The appointment follows a controversy in the run-up to the Games over travel arrangements for the basketball teams.
The women have been runners-up to the United States at the past three Games but despite their success flew to London economy class while the men, who have never medalled, went business.
The arrangements were slammed by Australian media and politicians and the country's basketball governing body said it would review its policy.
Gender was also an issue in the selection, with five time Olympian beach volleyballer Natalie Cook saying jokingly last week that she would stage a sit-down protest if another man was selected.
The last Australian woman to lead out the team was diver Jenny Donnet in Barcelona in 1992.