The reality TV star was charged following the crash that killed co-star Chris "Willow" Wilson in February 2022.
Wearing a light blue shirt and blue jeans, Wright appeared calm when he faced the Supreme Court in Darwin on Monday.
The court was silent before three counts of attempting to pervert the course of justice were read out for his arraignment and he pleaded not guilty to each charge.
Mr Wilson's widow Dani Wilson sat on one side of the courtroom and Wright's supporters including his wife Kaia, who he kissed during an adjournment, were on the other side.
The crash in remote West Arnhem Land in 2022 killed Mr Wilson, with pilot Sebastian Robinson seriously injured.
Mr Wilson was hanging from a sling under the helicopter to collect crocodile eggs when the crash occurred.
The trial before Acting Justice Allan Blow will begin after he hears legal arguments.
A jury is set to be empanelled on Wednesday, with opening statements from the prosecution and defence to follow.
The trial is expected to take up to four weeks and hear from about 25 witnesses.
The charge of attempting to pervert the course of justice carries a maximum penalty of 15 years' jail in the NT.
An Australian Transport Safety Bureau report into the 2022 accident found the chopper's engine stopped mid-flight because of a lack of fuel.
Wright rose to fame starring in National Geographic's Outback Wrangler and Netflix series Wild Croc Territory.
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