Landscaping around the house will be overseen by Sir Edmund's daughter Sarah and granddaughter Anna Boyer.
Gail Thomson, who heads a trust set up to restore the home and use it as a leadership centre, said: "We are trying to keep the house as close to the original as we can."
She was the Crown-appointed commissioner at the school when it was learned that the Hillary property had been sold and a new house was going to be built on its site.
She saw the 1956 house's potential to inspire students, and the property's new owner, Terry Jarvis, gave it to the school.
It was transported for free by Andrews Housemovers.
Ms Thomson said the trust was formed so the project would not be a drain on the finances of the decile 1 school of about 1200 students.
The project would cost a total of nearly $400,000.
"We are still fundraising, and need about $50,000."
Original kitchen fittings have been used, but restoration costs were pushed up by the need to meet Ministry of Education building standards.
The trust does not have memorabilia or books related to Sir Edmund's life for the new study and will seek donations of items.
Ms Thomson said it was hoped to have the official opening on May 29 - the 60th anniversary of the day Sir Edmund and Sherpa Tenzing Norgay became the first to reach the summit of Mt Everest.
The school also opened on that day in 1966.
The collegiate's middle school principal and trust member, Kallie Ngakuru-Syder, said pupils were getting excited as the building work neared completion.
The house would be available to the community as well as pupils and one of the trust's roles was to develop programmes in leadership and motivation.
