However, they finished last of the eight sides in 2017 and sixth this year, meaning Vettori's future was certain to come under scrutiny in a ruthless competition.
The RCB roster for 2018 was also perceived as competitive, boasting international talent such as AB de Villiers, Quinton de Kock and Moeen Ali and New Zealanders Brendon McCullum, Tim Southee, Corey Anderson and Colin de Grandhomme.
The franchise finished seventh and third in 2014 and 2015 respectively under Vettori's watch.
Sources said the 39-year-old had formed an excellent working relationship with RCB and Indian captain Virat Kohli during his five seasons in charge. He had also played for the franchise previously.
In a statement, RCB chairman Sanjeev Churiwala said it had been a great eight-year journey with Vettori.
"We wish him the very best for all future endeavours."
Kirsten added it was a "privilege" working under Vettori last season.
"I look forward to continuing the journey with RCB and doing my best to help the franchise reach its potential. I want to thank the team management for considering me in a leadership position ... and I look forward to a successful few years."
The RCB decision completes a difficult year on the coaching front for Vettori.
His Middlesex side finished ninth and last in the South Group of England's Vitality Blast T20 competition, and the Brisbane Heat were seventh of eight teams in Australia's Big Bash League.
However, he took the Heat to the semi-finals the previous season, and their brand of cricket has brought in bumper crowds for home games at the Gabba.
Vettori will resume his role at the Heat this summer after a stint as Rajshahi Kings coach in the Bangladesh Premier League during November and December.
