The second Test starts in Durban on Friday, with the third Test in the four-match series scheduled for Cape Town from January 2. South Africa won the first Test by 189 runs.
Left-arm wrist spinner Adams replaces left-arm finger spinner Robin Peterson, while batsman Kirsten comes in for fast bowler Garnett Kruger.
Adams has played 43 Tests and taken 132 wickets at an average of 31.15 but he has struggled with a hand injury this season.
Kirsten, a stalwart of 95 Tests in which he has scored 6866 runs at an average of 44.87 with 19 centuries, withdrew from the first Test to be with his wife at the birth of the couple's first child.
"Paul Adams is fit again and it was encouraging to see him put in a good performance for the KwaZulu-Natal Invitation XI against SA Schools (in Durban on Sunday),"
Adams took one for 28 from 10 overs in the limited overs match.
The axing of Peterson was expected after the world record 28 runs Brian Lara plundered off one of his overs in the first test in Johannesburg.
"As far as Robbie Peterson is concerned, he is an exciting young talent on a steep learning curve who came up against one of the world's great batsmen in top form at the Wanderers," Henry said.
"Knowing him, he would have learnt from that experience and will come back a better player."
Squad: Graeme Smith (captain), Paul Adams, Mark Boucher, Herschelle Gibbs, Andrew Hall, Jacques Kallis, Gary Kirsten, Neil McKenzie, Makhaya Ntini, Andre Nel, Shaun Pollock, Jacques Rudolph, Martin van Jaarsveld.