The 21-year-old, who played Super Rugby in 2017, has committed to the Highlanders despite still have a year to run on his Australian contract.
Lomax is the son of former Kiwis rugby league prop John Lomax, who played 15 tests for the Kiwis between 1992-98.
Lomax grew up playing league in Wellington but switched to rugby when his family moved to Australia.
He was a member of the 2015/16 Australian under-20 team and was named the Australian under-20 player of the year in 2016.
Lomax was named in Michael Cheikas' original 48-man squad for 2017 before withdrawing.
"I grew up in New Zealand and as an aspiring rugby player the chance to play for a New Zealand Super Rugby club was too good an opportunity to turn down," Lomax said in a statement.
"As a young prop I can't wait to get to the Highlanders, they have an awesome culture there and I just want to immerse myself in it and learn as much as possible."
Highlanders chief executive Roger Clark has been impressed by the young man.
"Throughout our dealings with Tyrel he has shown himself to be a mature young man with a real determination to learn and improve," he Clark said.
"He has a real desire to go as far as he can in the game. He will fit in well at the Highlanders and we would like to think this is just the start for Tyrel - we believe he has a very bright future in front of him."
Highlanders coach Aaron Mauger is delighted the young prop has committed to the Highlanders.
"Clearly we see Tyrel as an exciting future prospect for the club, a strong ball carrying prop, we think his game will benefit from our environment and he will add depth to our squad."