Mehran Azami on Monday appeared in the Melbourne Magistrates Court on multiple charges connected to the plot.
Azami pleaded guilty to 19 charges of importing restricted goods, including knives and stun guns, local media said.
A teenager from the UK has also admitted involvement in the plan which was targeting police at the parade.
Police say they prevented the attack, planned for Melbourne, when Azami and others were arrested in anti-terrorism raids.
A UK court has heard that several of the alleged plotters were supporters of the Islamic State militant group.
Anzac Day, held on 25 April each year, commemorates the Australian and New Zealand Army Corps' World War One battle in Gallipoli, with this year marking its centenary.
Azami was remanded in custody until October, said the Australian Broadcasting Corp. (ABC).
He was 19 when he was arrested after police launched counter-terrorism raids in April.
The Melbourne Magistrates Court had previously heard Azami had given some weapons to Harun Causevic and Sevdet Besim, who are charged with conspiring to plan the attack, reported The Australian.
Defence lawyer Charles Atlas has previously said Azami was suffering from a mental illness and was being kept at a psychiatric facility.
A teenager from Blackburn in the UK earlier this month pleaded guilty to one count of inciting terrorism by encouraging the murder of police officers during the parade.
The 15-year-old appeared at the Old Bailey via video link from Manchester Crown Court, speaking only to enter his plea.
He could not be named for legal reasons.
The Old Bailey heard the boy, who was 14 at the time, sent thousands of instant messages to 18-year-old Besim in Australia over a 10-day period in March.
The boy sent a message to the older teenager suggesting he got his "first taste of beheading," prosecutor Paul Greaney QC said, to which Besim replied that this seemed "risky".
According to the Australia government, at least 100 Australians are fighting with terror groups in the Middle East, and another 150 people in Australia are known to be supporting such groups.

The game at Grace Road was due to get under way at 18:30 BST.
But umpires Russell Evans and Rob Bailey ruled the ground was unfit for play after a late-morning inspection.
The two clubs were also hit by the weather on Wednesday when their One-Day Cup match at New Road was rained off.
A statement on the club website said: "Aylestone was affected by flash flooding on Tuesday and the Fischer County Ground resembled a lake with the water subsequently gathering in the far corner of the ground.
"Further rain has fallen either side of that particular deluge and although the club brought in heaters to try to dry everywhere out, conditions remain sodden and unfit."
Worcestershire will have Moeen Ali available for Saturday afternoon's home T20 Blast game against Nottinghamshire, for whom fellow England Test player Alex Hales is scheduled to appear.
"It's good when you've got England players playing," said Worcestershire director of cricket Steve Rhodes. "It is a big bonus having Mo available.
"It is a sensible thing to do by the ECB. They want our Blast tournament to have good exposure and become a really good domestic tournament.
"Just as in the Caribbean Premier League, Big Bash and IPL, a lot of the home international players play in those tournaments."
Worcestershire will give fitness tests to skipper Daryl Mitchell and paceman Matt Henry, who have both been sidelined with rib injuries.
A man has pleaded guilty to supplying weapons for a foiled terror plot at an Anzac Day remembrance parade in Australia.
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Friday's T20 Blast match between Leicestershire and Worcestershire was called off almost seven hours before the scheduled start after heavy rain left the outfield "resembling a lake".