The actor was killed by his own car at his home in Los Angeles in June.
It struck him after rolling backwards down the steep drive, pinning him against a brick postbox pillar and a security fence.
Court records show Victor and Irina Yelchin filed to become administrators of their son's estate on Friday.
The filing states Yelchin left behind at least $641,000 (£486,000) in personal property and had $731,000 (£554,000) in equity in his home.
Yelchin was best known for playing Pavel Chekov in the new Star Trek films.
TMZ reports that Yelchin's parents plan to file a wrongful death lawsuit against Fiat Chrysler, which made the Jeep that killed their son.
They are expected to announce their intentions to file the suit at a press conference on Tuesday.
In April, the company  recalled 1.1m vehicles worldwide over the risk they could roll away after drivers exit.
The vehicle that killed Yelchin, who was 27 years old, was one of those subject to a recall because the gear shifters confused drivers, causing the vehicles to roll away unexpectedly.
Fiat Chrysler offered their sympathies to Yelchin's family in a statement, but said it could not comment on their plans for a lawsuit.
The company added it was speeding up its recall of the vehicle.
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The nine members of the team, who will compete across the four events, all won medals at last year's World Championships while two have already won Paralympic gold in the sport.
Tom Aggar won single sculls gold in Beijing while Pam Relph was part of the victorious mixed coxed four in London.
Rachel Morris will compete in her second sport after winning handcycling gold in Beijing and bronze in London.
The 37-year-old double amputee transferred to rowing in 2013 and won silver at the 2015 World Championships in France.
Relph, 26, is the only remaining rower from her 2012 boat and teams up with debutants Grace Clough, James Fox, Daniel Brown and cox Oliver James.
The boat is unbeaten since the 2011 Worlds and the current crew are two-time World champions.
"The team that has been selected is far stronger than any I have been a part of in my six years of rowing for GB," Relph said.
There is also a new look in the double with Laurence Whiteley and Lauren Rowles hoping to make an impact in their first Games.
Whiteley, 24, spent two years waiting for a suitable partner to come along but his patience was rewarded when wheelchair racer Rowles, 18, who has just finished her A Levels, tried out early last year.
The partnership yielded a silver medal at the 2015 Worlds in their first major competition together.
Squad: Tom Aggar, Rachel Morris, Laurence Whiteley, Lauren Rowles, Pam Relph, Grace Clough, James Fox, Daniel Brown, Oliver James.

The 59-year-old actor and presenter has launched a petition to prevent buildings being demolished to make way for a new station.
A planned Crossrail 2 connection at Tottenham Court Road will see two new access points built in Soho.
Fry, who is chairman of Save Soho, warned the area "could change dramatically".
He said the group did not oppose Crossrail 2.
But he said: "Soho is not just a metropolitan enclave... it is a focus, a magnet for the young, creative and open-minded around the country.
"The new threat to Soho's authentic soul coming from Crossrail 2 is a real and urgent issue."
London Mayor Sadiq Khan has warned that London's transport network will grind to a halt due to overcrowding unless the government backs Crossrail 2.
Construction could start in the early 2020s and the railway could be open by 2033.
A preferred route for a proposed Â£20bn Crossrail 2 scheme, running north-south through London was approved in 2014.
Crossrail 2 bosses say improvements will reduce crowding on the busiest part of the Northern line during peak periods by approximately 30%.
Anton Yelchin did not write a will before he died and left behind a $1.4m (£1.06m) estate, according to court documents filed by his parents.
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Great Britain have named an experienced rowing squad for the Rio Paralympics.
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Stephen Fry has said Crossrail 2 poses a threat to Soho's "authentic soul".