The 47-year-old Outback Wrangler star just missed his wife Kaia giving birth to his third child, a son, on Sunday before he was released early on Monday.
He has said he plans to appeal his convictions.
Wright was sentenced in December to 10 months in prison, suspended after five months, with a two-year good behaviour period.
Having served the five months, Wright was eligible for release from Darwin Correctional Centre on Monday.
Despite applications for early release on compassionate grounds, Corrections Commissioner Matthew Varley said the crocodile wrangler would be required to serve the full term imposed by the court.
"Finally home with my family after one hell of a fight," Mr Wright posted on Instagram on Monday.
"Didn't quite make the birth of our beautiful boy Sterling, but Kaia Wright did an incredible job."
The Outback Wrangler star's friend and co-star Chris "Willow" Wilson was killed in the February 2022 crash that left pilot Sebastian Robinson a paraplegic.
It happened during a crocodile-egg collecting trip in Arnhem Land while Mr Wilson was slung on a line below a helicopter to drop onto nests in remote swampland.
Wright was accused of lying to crash investigators about the amount of fuel in the machine, of trying to get Mr Robinson to falsify flying hours and of asking a friend to "torch" the helicopter's maintenance release.
On August 29, a jury found him guilty on the first two counts but could not reach agreement on the third allegation.
Prosecutors alleged Wright was worried investigators would learn his choppers' flying-hour meters were regularly disconnected to extend hours beyond official thresholds and paperwork was falsified to match.
The prosecution did not allege he was responsible for the helicopter crash, Mr Wilson's death or Mr Robinson's injuries.
Acting Justice Alan Blow said Wright made unlawful attempts to prevent charges being laid against him and his helicopter company Helibrook despite being the holder of an air-operating licence that carried safety obligations.
It was highly likely the helicopter that crashed should not have been flying after exceeding its maximum flight time of 2200 hours, at which it should have been retired or undergone a costly overhaul, the judge said.
"It is clear you had reason to fear that a thorough investigation might reveal that the 2200-hour limit had been exceeded," he said.
The charge of trying to get Mr Robinson to falsify flying-hour records by putting hours from the crashed chopper onto the pilot's own machine was a "serious attempt to pervert the course of justice", the judge said.
In sentencing, he found Wright had contributed substantially to the community as a successful operator of tourist ventures and supporter of charities and conservation causes, noting impressive character references.
The adverse and widespread publicity surrounding Wright's case had led to some of his businesses to the point of failure, the judge noted.
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