Wright, 43, who "strenuously denies any wrongdoing", was granted bail to appear at Darwin Local Court on Wednesday.
The crocodile trapper-turned-media personality is accused of perverting the course of justice and destruction of evidence stemming from the February crash that killed Chris Wilson, 34, when the helicopter crashed into trees and the ground.
Wright is also accused of fabricating evidence, interfering with witnesses, making a false declaration and two counts of unlawful entry.
The father of two flew from Sydney on Tuesday morning after Northern Territory police issued an arrest warrant a day earlier.
Wright later turned himself in at Darwin Police Station before police moved him to a Palmerston watch house about 20 kilometres south, and was later released on bail.
His bail conditions include a direction to not contact certain people and to reside at a prescribed address.
Mr Wilson died when the Robinson R44 helicopter he was attached to by a 30-metre line using a harness crashed in west Arnhem Land.
His body was found 40 metres from the main wreckage at the King River crash site, a preliminary Air Transport Safety Bureau report revealed in April.
Mr Wilson, also a father of two, was dangling the strap to harvest eggs from crocodile nests in swampy areas while the helicopter hovered above.
The crashed helicopter was one of three collecting eggs on the day. It was found by one of the other crews after failing to respond to radio calls.
Pilot Sebastian Robinson was seriously injured and airlifted to Maningrida, before being transferred to hospital in Darwin.
A preliminary ATSB analysis of the site indicated the accident happened when the helicopter's main rotor blade struck and cut through a tree trunk multiple times before the aircraft hit the ground.
Initial assessments indicated the engine had stopped before the helicopter hit the ground.
An examination found there were no defects likely to cause the engine to stop, and no visible damage to the tail rotor blades and drive system.
It is understood the chopper was certified by independent aviation experts as safe to operate just weeks before the crash.
In a statement on Monday, a representative for Wright said "Matt strenuously denies any wrongdoing".
"What happened was a tragic accident that took the life of a close mate," the representative said.
"His immediate concern following the accident was the condition of the two team members on board at the time.
"The next priority was ensuring the other helicopters and team members at the site weren't at risk and that the location was safe."
Earlier, the star's minders pushed and shoved media as they escorted the crocodile trapper through the Darwin airport to a waiting Range Rover.
One TV cameraman who said he was forcefully shoved later gave a statement to police.
Outback Wrangler is an adventure TV series filmed in remote Top End locations that airs in Australia on Nine and Netflix and in more than 90 countries.
The show chronicles the capture and transport of dangerous animals that pose a threat to people, including crocodiles and buffalo.
NT police officer Neil Mellon and pilot Michael Burbidge have also been charged in relation to the helicopter crash.
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