Kohli stepped down as India's Test skipper a day after the 1-2 defeat to South Africa in their three-match red-ball series. The BCCI haven't announced a new Test captain yet.
Kohli also released a statement on social media to explain his decision.
After taking over Test captaincy from MS Dhoni in the middle of the 2014-15 Australia tour, Kohli led India to the no. 1 Test spot and also registered 40 wins in 68 games with a win percentage of 58.82 - the most by an Indian captain.
McCullum captained New Zealand in 31 Tests, winning 11 games, losing 11 and drawing nine. His win percentage of 35.48 is the third-highest for any Blackcaps captain with over 10 matches as Test skipper.
Earlier, Kohli had also stepped down from T20I captaincy after the T20 World Cup last year. He was also removed from ODI captaincy after the T20 World Cup. The BCCI announced Rohit Sharma as India's new full-time white-ball captain in December last year.