Warren Lee, 53, Aesoon Lee, 52 and their daughter Julia Lee, 20, died in the collision north of Tokoroa on Tuesday.
Their 18-year-old son remains in a critical condition in the intensive care unit at Waikato Hospital.
He was not aware the crash had killed his family, a hospital spokeswoman said.
Mr and Mrs Lee were American citizens living in Hong Kong, while Ms Lee had been living and studying in Massachusetts. She was due to start studying at the University of Auckland in a few days' time.
The family had come to New Zealand to help Ms Lee settle into her new home before they returned to Hong Kong. She was driving at the time of the crash.
Ms Lee was yesterday described as "a young woman of tremendous vibrancy and compassion" by her former university, while friends mourned her loss on social media.
Lucy Tang paid tribute to her close friend on Facebook, saying: "The impact you have made on the past 10 years of my life cannot be described with words.
"Thank you for all the rainbows and sparkles, it's not easy saying goodbye to a best friend."
She finished by saying: "Lees forever in my heart. 18.2.15."
Ms Lee was a computer science major in the College of Liberal Arts at Tufts University, Massachusetts. A message from university president Anthony P Monaco, posted on the Tufts website, said she was about to begin a study abroad programme at the University of Auckland through Arcadia University in a few days' time.
"This loss is a tragedy for all who knew and loved Julia and her parents, and for Julia's faculty members, advisers, classmates, and friends," he said.
"This is also a loss for all members of the Tufts community.
"Julia was a young woman of tremendous vibrancy and compassion, and she will be deeply missed."
A post on the university's LGBT Centre's Facebook page said it was "saddened by the sudden loss of Tufts junior Julia Lee", and described the death of Ms Lee and her parents as an "immense loss".
Two services were scheduled to be held at the university's Goddard Chapel, and information was provided to students and staff about how to access counselling and support services.
On Twitter, Roy Yang said: "Experienced death of a friend for the first time..puts perspective in a lot of things. R.I.P Julia Lee. I know you're in a better place."
Another user, Jose C Hernandez posted: "I feel so sad for the death of Julia Lee and her relatives. My sincere condolences to the #Tufts community and her friends."
A University of Auckland spokeswoman expressed its "profound sympathy" to the family and friends of the Lee family.
"Out of respect for the family we will not be commenting further at this time."
The crash happened about 3.45pm on Tuesday on State Highway 1, north of Tokoroa, when the car Ms Lee was driving crossed the centre line and collided head-on with a logging truck.
Her brother was in the front passenger seat, while their parents were in the back. It is understood Mr and Mrs Lee were not wearing seatbelts.
Investigations into the cause of the crash were continuing.
- Additional reporting: Sophie Ryan
By Patrice Dougan of NZME. News Service
