In a written statement to the Rotorua Daily Post, Board of Trustees chairwoman Ruiha Ruwhiu said the board had accepted Mr Fairhall's resignation with regret.
"The employment investigation has ceased as Mr Fairhall has tendered his resignation, effective immediately, in order to pursue other opportunities.
"We would like to acknowledge that Uenuku Fairhall has made a significant lifetime contribution to our kura, our students and our community and to Maori education.
"The resignation has been announced to kura whanau today . Parents of the wider whanau received a panui (notice) from the board last week about the early return of those on the trip and that there was a matter that was being investigated. Parents have been supportive."
Tuparahaki McAllister had agreed to continue as acting principal until the board worked through the appointment process, she said.
"Now that the school has reported the matter to the Education Council, the kura's official processes have ended. Our main focus continues to be on ensuring that all of our students are well supported and all students continue to receive a high quality education during this transition stage until a new principal is appointed."
Mr Fairhall told the Rotorua Daily Post his resignation was "for the good of the kura" and would allow it to move forward.
"I've enjoyed my years at the kura and I am grateful for the people I've worked with... Up until recently it has been a positive experience and I wish the kura all the best."
The trip to Mexico, involving 21 students and three teachers, including Mr Fairhall, was meant to last 12 weeks but was cut short by five weeks last week.
The three-yearly trip, which sees students billeted with Mexican families to ensure immersion in the Spanish language, has become a part of the school's culture.
