Southee, who was omitted for the game at University Oval as New Zealand opted for two spinners, will replace Boult in the starting side.
Batsman Neil Broom would also make his test debut in place of the injured Ross Taylor, Southee said, though they had still not finalised the remainder of their team for the match at the Basin Reserve starting on Thursday.
"There are still a couple of question marks around a couple of the players," Southee told reporters on Wednesday.
Much of the debate in New Zealand centres around whether Jeetan Patel or Mitchell Santner would be the first-choice spinner if the hosts, as expected, revert to a three-pronged pace attack.
Matt Henry looms as the most likely third seaming option for the hosts along with Southee and Neil Wagner, with the wicket at the Basin Reserve offering a green tinge on Wednesday after several days of heavy rain and inclement weather in Wellington.
Wagner had a heavy workload in Dunedin, bowling 58 overs, with Boult only able to bowl 15 in South Africa's second innings before he left the field.
Southee said the left-armer had dialed it down in training in the leadup to the test.
"Neil didn't bowl a hell of a lot between Dunedin and now," Southee said. "He had a bit of a bowl today just to freshen up and bowl a bit of the stiffness out of his legs."
Southee added that losing Taylor would leave a large hole in the middle order, but they had faith the 33-year-old Broom would comfortably step into the number four spot.
"Neil has got the opportunity to perform now. He has been dreaming about this for a long time," Southee added.
"He has shown glimpses this summer that he is capable of performing at the international level, so we're looking forward to seeing what he does."
(Reporting by Greg Stutchbury; Editing by Ian Ransom/Peter Rutherford)
