The 29-year-old Waikato Chiefs playmaker has played 61 tests for New Zealand and was Robertson's first-choice flyhalf last year until losing the spot to Beauden Barrett.
"He has an incredible skill set and the ability to change a game," said Robertson.
"He is just continuing to get better and better, which makes him a critical signing for us heading into the next Rugby World Cup and beyond."
McKenzie's four-year contract extension comes after a high level of interest in the speedy playmaker from overseas clubs, Chiefs coach Clayton McMillan said.
He will hope to be a part of New Zealand's Rugby World Cup squad in 2027 and play against the touring British & Irish Lions in 2029.
"I'm extremely motivated to win a championship with the Chiefs and ultimately hope to be a part of a successful Rugby World Cup in 2027 and campaigns beyond that," said McKenzie.