Bird was held back when other Test team members left for South Africa on Wednesday. But after back-to-back days of net bowling, he was given the approval by Australian coaching staff on Thursday.
Shaun Marsh, who is battling a calf injury, has yet to prove his fitness for the tour.
The first Test at Centurion begins February 12. The second Test will be played beginning February 20 in Port Elizabeth and the third from March 1 in Cape Town, followed by three Twenty20 matches.
Australia begin their tour with a four-day match beginning next Wednesday at Potchefstroom.
Jackson Bird cleared for Test series against South Africa
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