Batsman Fleming is quitting one-day internationals but plans to continue in the Test side for the time being.
"The selectors are looking to the future and have recommended that Daniel assume captaincy of the Test team as well as the one-day team," NZ Cricket chief executive Justin Vaughan said in a statement on Wednesday.
Fleming, 34, said it was the right time to retire from one- day internationals, and signalled that his Test career may also be coming to an end.
"I shall continue playing Tests as long as I have the desire and skills required to contribute. However, it is likely that the coming New Zealand summer will be my last home series," he said in a statement, adding that he would have liked to carry on as Test captain.
Vettori, who already skippers the one-day side and has been Fleming's Test deputy, is currently leading New Zealand at the Twenty20 World Cup in South Africa.
New Zealand tour South Africa and host England this season.
Fleming captained the New Zealand Test team to 28 wins and 25 draws in 80 matches over 10 years.
He played 280 one-day internationals, 218 as captain, leading New Zealand to 98 wins and scoring 8,037 runs, a national record.
Fleming has been playing for English county Nottinghamshire and has been strongly linked with the rebel Indian Cricket League
