Gibbes has been working as an assistant coach over the past two seasons, following extensive overseas coaching experience.
"Being part of the organisation for the past two years has given me an appreciation for what's been built here and how this team has grown into a consistent, competitive unit.
"My job now is to help maintain that consistency and keep pushing to unlock the full potential of this team. We have a strong foundation and a lot of talent, so I'm excited about what we can achieve."
An eight-Test All Black, Gibbes played 68 games for the Chiefs between 2001-08 and 64 times for Waikato between 2000-07 while also playing nine times for the Māori All Blacks.
After retiring from playing, he coached at Leinster, Clermont Auvergne, La Rochelle and Ulster. In 2018, back in New Zealand, he coached Waikato to the NPC title and subsequently became the coach of the New Zealand Under-20s.
Chiefs chief executive Simon Graafhuis said the move was a natural progression for Gibbes and the coaching group.
"He understands the Chiefs fabric, the importance of our provincial unions, and the aspirations of the team and community."
Outgoing coach McMillan said the team was in superb hands.
"Jono brings a wealth of experience, leadership and a strong connection to this region.
"The coaching, management and playing group has a lot of continuity and cohesion which is a strong foundation to build from. I have no doubt this group will lead the Chiefs to great things and continue to excite and inspire our loyal supporters."
New Zealand Rugby general manager of professional rugby and performance Chris Lendrum said Gibbes was highly experienced, with a deep knowledge of rugby environments in Ireland, France, and New Zealand.
"He has a deep connection and understanding of the game in Aotearoa and his record and reputation are compelling."