McMillan was appointed to the interim role this year while regular coach Warren Gatland leads the British & Irish Lions to South Africa.
McMillan said he was 'stoked' to sign with the Chiefs for another two years and grateful for the opportunity.
He said the Chiefs had shown faith in his ability, even at such an early stage, but that demonstrated the clear vision he was excited to be part of.
"I have already formed a good relationship with Gats. He was extremely welcoming in 2020 and allowed me to come in and see the organisation from the top down.
"We have caught up numerous times since, and we will continue to build on our relationship," he said.
Working alongside the former All Black, and Wales coach, was a significant attraction for McMillan in the first place.
"He is one of the world's most successful coaches. I have always been a head coach, so in many respects, I will relish the opportunity to step back and be mentored by somebody of his experience and stature.
"It is only going to help me in my coaching journey and [is] one I am exceptionally grateful for," he said.
Chiefs chief executive Michael Collins welcomed McMillan extending his contract.
"Clayton has a great record of results from coaching the Bay of Plenty Steamers and the Māori All Blacks. He is a proven leader who understands our Chiefs culture.
"Clayton and Gatty have formed a good working relationship. He has already had a positive impact since he joined us," he said.
Gatland said he was pleased to have McMillan continue in the coaching group.
"He is extremely well respected in the game and what he has achieved with Bay of Plenty, and the Māori All Blacks gives him the credit he deserves coming into these roles as head coach for this season, and continuing as assistant coach when I return," he said.
The Chiefs play their first game of the 2021 campaign on March 5 against the Highlanders in Hamilton.