The pair were not expected to arrive on the tour of England until after the completion of this weekend's inaugural three-day warm-up match against Derbyshire.
But McCullum and Taylor will now have more time to get used to English conditions before the two-match Test series gets underway at Lord's later this month.
McCullum is due to join the team during their training session in Derby on Friday with Taylor following within 48 hours.
"McCullum will join the team in Derby later tomorrow (Friday) and Taylor is expected to arrive over the weekend."
Taylor was replaced as New Zealand captain by McCullum in controversial circumstances during the tour of Sri Lanka last year.
McCullum recently scrapped plans to sue former New Zealand skipper John Parker after receiving an apology over claims he said attacked his integrity.
Parker alleged McCullum, 31, was aware Taylor was going to be axed as skipper late last year, despite the batsman's insistence he knew nothing about the decision.
Taylor's demotion opened deep rifts within New Zealand cricketing circles, with many former players saying he had been poorly treated.
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