JOIN USTaylor, who has played 30 tests and 107 limited-overs internationals, was appointed this week to lead New Zealand in all forms of the sport. Vettori resigned the test captaincy earlier this year and will no longer play ODI and Twenty20 internationals.
New Zealand Cricket has been criticized for the length of time it took to decide between Taylor and the more experienced McCullum, helping to create and impression of rivalry between the two.
McCullum said in a radio interview that he and Taylor were "good enough mates" to resolve any differences.
"Obviously I was disappointed to miss out on something that I desperately wanted but ultimately you've got to move on and I do wish Ross all the best and I definitely support him along that journey," McCullum told Radio Sport.
"I had my opportunity to present my case and to show what I thought was the way forward for New Zealand Cricket and ultimately they decided to go another route and you can't argue with that," McCullum said.
Coach John Wright has expressed the hope McCullum will accept the vice-captaincy under Taylor. McCullum, 29 and a veteran of 57 tests and 192 ODIs, said he hoped to continue playing international cricket for another five or six years.
He said he was still eager to contribute to the New Zealand team despite the rejection of his claims to the captaincy.
"Inside the first 24 hours when you suffer that disappointment you go through a range of different emotions and different thoughts," he said. "It took me about 24 hours for everything to come clear and that I have a huge opportunity to contribute to this team.
"It is still for me about playing for my country. It always has been. There may be a misconception out there that I'm not like that but I'm incredibly passionate about playing for my country and that will never change."