"Kirsten has signed the contract, he will take over the new assignment on March one next year," board secretary Niranjan Shah told AFP.
The deal was sealed after all the issues relating to Kirsten's appointment were sorted out Tuesday, paving the way for the former opener to occupy the hot-seat, vacant since the exit of Australian Greg Chappell in April last year.
Shah said Kirsten will meet the players in Bangalore, venue for India's third and final Test against Pakistan on December 8-12.
"Kirsten will be spending a couple of days with the Indian team in Bangalore during the third Test against Pakistan," he said.
"He will be with the Indian team in Australia as a consultant for a couple of weeks before taking over full-time in March when India host South Africa."
India are to leave for Australia on December 17 to play four Tests and a limited-over tri-series, with Sri Lanka as the third team.
Kirsten, 40, told the cricinfo.com website that he would be honoured to take charge of the Indian team.
"It is a huge honour and I'm looking forward to the challenge with as much enthusiasm as any challenge I've ever faced. I know how big the job is and I know it won't be easy, but it's also something I really want to do, and do well," he said.
Kirsten, who who quit international cricket in 2004 after scoring 7,289 runs in 101 Tests, also said he was excited about the prospect of India facing his home country in his first assignment as coach.
"That's exciting. I really don't think it will feel strange or odd. I will be doing everything I can to help India win. But Australia comes first and everybody's energy must be focused on producing success on what is the hardest tour in cricket," he said.
Kirsten's appointment caps months of speculation over who would be handed over the high-profile job following Chappell's exit in the wake of India's shock first-round exit from the World Cup in the Caribbean.
Three men were in temporary charge since then after South Africa's Graham Ford, who coaches English county team Kent, turned down an offer from the BCCI.
Former all-rounder Ravi Shastri managed the team for the tour of Bangladesh in May and Chandu Borde, 73, took over during the visit to Ireland and England from July to September.
Former Mumbai first-class cricketer Lalchand Rajput then took charge for the inaugural Twenty20 World Cup in South Africa in September, which India won, and continued for the home one-dayers against Australia and Pakistan.
Rajput will officially be assistant coach in Australia but will resume the responsibility of head coach.