The batsman served as the vice-captain under Vettori and his appointment was widely expected.
"I've learnt a great deal about leadership, having played under Dan Vettori, and feel ready to take on what is one of the highest honours in New Zealand sport," said Taylor, 27, who has played 30 Tests, with has an average of 41.12, and 107 one-day internationals, averaging 36.8.
John Wright, the Black Caps coach, John Buchanan, the director of cricket, and Mark Greatbatch, the acting selection manager, had all backed Taylor's appointment.
"We wanted to make sure the right people were involved and that we appointed the right man for the job," Justin Vaughan, the chief executive of New Zealand Cricket, said.
"I'm sure we have done that."
Vettori stepped down after guiding New Zealand to the World Cup semi-finals to concentrate on his goal of becoming the second Test player behind India's Kapil Dev to take 400 wickets and 4,000 runs. The 32 year old has already scored 4,167 Test runs and has 345 wickets.