Ross Taylor, 28, was axed after rejecting an offer to remain Test skipper while handing limited overs duties to McCullum, New Zealand Cricket (NZC) chief executive David White said.
White denied coach Mike Hesson had lost faith in Taylor's captaincy after a string of poor results since taking over in June 2011, but said he was concerned the skipper's duties were affecting his batting.
"He felt it would be better for Ross to focus on his game," White told reporters.
"It was felt that the workload for a young captain was a lot." Despite his team's woes, Taylor has been New Zealand's best batsman in recent Tests, averaging 43.57, and his absence will be sorely felt against South Africa, who top the Test rankings while New Zealand are placed eighth.
"It's not ideal and we would be a stronger team with Ross in it but we respect his wishes," White said.
White said Taylor would take a break from cricket but was expected to be available for the home series against England beginning in February. He said he regretted that Taylor's departure, which came after a review of the Sri Lanka tour, was accompanied by a week of speculation and rumour over NZC's intentions, conceding the matter could have been handled better.
Opener McCullum, 31, who will become New Zealand's 28th Test captain, is widely seen as offering more attacking tactical nous than the conservative Taylor. But Taylor's treatment has sparked fury in New Zealand cricketing circles, with batsman Jesse Ryder tweeting this week that it "angers me watching Ross Taylor getting dumped on", and calling on NZC to support him.
Retired allrounder Scott Styris also took to the the micro-blogging site saying "any goodwill/public support from fans and supporters towards the Black Caps after their brilliant win in SL (Sri Lanka) has now gone!".
TVNZ reported on Thursday that batting great Martin Crowe has resigned from his post as NZC talent scout in protest at the organisation's actions.
Fairfax Media columnist Ben Stanley wrote after the announcement Friday that the episode had been "an absolutely appallingly executed operation by a national sporting body and its board". Stanley added that the South Africa tour beginning later this month, which includes two Tests, three one-day internationals and three T20 internationals, was now "looming as a potential massacre".
New Zealand lost seven of 13 Tests under Taylor's captaincy, winning four and drawing two. Two of the wins were against lowly Zimbabwe, with the highlights of his tenure a rare Test victory over Australia in Hobart in December last year and a series-levelling second Test victory over Sri Lanka in Colombo last month.
Over the same period, the Black Caps have lost one-day series to South Africa, the West Indies and Sri Lanka, with their sole series win against Zimbabwe.