Holland, who played his only two Tests in Sri Lanka in August 2016, has leap-frogged over fellow left-arm spinner Ashton Agar to be off-spinner Nathan Lyon's deputy.
The 21-year-old Richardson has had a taste of international cricket having made his One-day International (ODI) debut at the Gabba in Brisbane last Friday, taking 2-57 against England.
The selectors led by Trevor Hohns retained both Cameron Bancroft and Peter Handscomb despite underwhelming displays during the victorious 4-0 Ashes campaign against the Englishmen.
The squad features five players with Test match experience in South Africa, with skipper Steve Smith, David Warner, Lyon and Shaun Marsh playing in 2014, while left arm paceman Pat Cummins made his debut as a teenager at the Wanderers.
The first Test starts on March 1 in Durban before matches in Port Elizabeth (March 9), Cape Town (March 22) and Johannesburg (March 30).
Meanwhile, Warner is the only member of the Test squad who will remain with the T20 unit, captaining the side in place of Smith. Smith has been given a break after scoring a mountain of runs in the Ashes.
The T20I squad boasts of some of Australia's most powerful batsmen, headlined by Chris Lynn, Glenn Maxwell, Marcus Stoinis and D'Arcy Short, the Big Bash League's leading run-scorer this summer.
Australia host the first leg of the T20I tri-series, squaring off against New Zealand at the Sydney Cricket Ground on February 3 then England at Blundstone Arena and the Melbourne Cricket Ground on February 7 and 10, respectively.
The series then travels across the Tasman Sea, where Australia take on the Black Caps at Eden Park on February 16 before the tournament final at the same venue four days later.
Those players not involved in the T20I squad will travel to South Africa in February 15 ahead of a three-day tour match in Benoni from February 22.
Test Squad: Steve Smith (Captain), David Warner (vc), Cameron Bancroft, Usman Khawaja, Peter Handscomb, Shaun Marsh, Mitchell Marsh, Tim Paine (WK), Mitchell Starc, Josh Hazlewood, Pat Cummins, Nathan Lyon, Jackson Bird, Jon Holland, Jhye Richardson.
T20 Squad: David Warner (Captain), Aaron Finch (vc), Ashton Agar, Alex Carey, Ben Dwarshuis, Travis Head, Chris Lynn, Glenn Maxwell, Kane Richardson, D'Arcy Short, Billy Stanlake, Marcus Stoinis, Andrew Tye, Adam Zampa.
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