Brierley, 83, pleaded guilty at a hearing on April 1 to three charges of possession of child sexual abuse material. Another 14 charges were withdrawn.
Today's hearing in Sydney was procedural. "The matter is in for first mention today to confirm the plea," his lawyer, Lisa-Claire Hutchinson, told the court.
"Mr Brierley is prepared to do that and is in a position to do so."
Hutchinson added that the lawyers on both sides were close to agreeing the facts and expect to do so by the next hearing, which was set for May 21.
Brierley did not appear in court but by video link from his lawyer's chambers.
Brierley was arrested at Sydney Airport on December 18 while preparing to board a plane to Fiji. The Australian Border Force, acting on a tip to New South Wales police, seized Brierley's laptop and other electronic devices.
Instead of flying to Fiji, Brierley was taken to a nearby Mascot police station before being bailed to his home in the exclusive Point Piper neighbourhood.
Brierley has been on bail since his arrest, with the same conditions continuing after his guilty plea. Those bail conditions have allowed him to stroll nearby Double Bay and drive around Sydney's eastern suburbs. Brierley has lived in Sydney for decades.
Brierley is one of New Zealand's best-known businessmen. He built a reputation as a formidable "corporate raider" who bought shares in undervalued companies, and by the 1980s had amassed an international portfolio that included prominent investments in Australia and the UK.
Brierley was once one of New Zealand's richest people — his fortune was recently estimated at $220 million — and his influence extended beyond the business world. He was a generous philanthropist who was closely involved with New Zealand cricket and ballet, and in 1988 was honoured with a knighthood.
The guilty plea has led to calls for Brierley to lose that title. The Department of the Prime Minister and Cabinet's honours committee is reviewing whether Brierley's knighthood should be stripped from him.