Maguire was given full backing by New Zealand Rugby League to take on the role. NZRL chief executive Greg Peters said he had no issues with Maguire holding dual roles with the Kiwis and the NRL side.
"We were aware when we appointed Michael that this was the likely outcome," said Peters.
"He made it clear to us from the outset that he wanted to coach in the NRL again as well as coach the Kiwis. He wants to develop a winning culture that takes us to the World Cup.
"We congratulate Madge on his appointment. He knows we have confidence in him being able to continue his vital role with the Kiwis in the current series against England and in the years to come."
Cleary is now expected to join son Nathan at the Penrith Panthers, who were yet to fill their vacant head coaching role.
If appointed, it will be the second time Cleary has taken the reins at the foot of the mountains. He was sacked by the club at the end of the 2015 season with the Panthers finishing 11th on the ladder just two points off the wooden spoon.