The public was told of the threat in March and formula was taken from supermarket shelves and held securely to prevent contamination.
In what became known as Operation Concord, 60 people were considered of significant interest and approached to be interviewed by police.
More than 2600 people were considered over the course of the investigation, which cost police $3 million, Mr Bush revealed.
On Monday, police acted on five search warrants in Auckland and Rangitikei District.
Police said they believed the arrested man acted alone and no one else has been charged.
Meanwhile, the testing regime on infant formula would continue. More than 150,000 batch tests have been carried out since the threat.
Prime Minister John Key said yesterday the threat had been extremely serious, despite the remote risk that it would be carried out. He was told on Monday night an arrest would be made.
"It is very good news that the police have followed up ... obviously I can't say too much because it is before the courts, but it will be a great relief if that is the individual in question."
Labour leader Andrew Little said it sounded as though the task facing investigators had been akin to looking for a needle in a haystack, and they should be congratulated.
Fonterra chief executive Theo Spierings thanked the Ministry for Primary Industries and police for their exhaustive efforts.
At the arrested man's court appearance, several company names were also suppressed.
According to court documents, the man "threatened expressly to endanger the safety of any person, namely infants, by releasing infant milk formula into the Chinese market contaminated with traces of 1080, with intent to cause Federated Farmers Incorporated to act in accordance with the will of [the man] to cause Federated Farmers to pressure the New Zealand Government to stop the use of 1080 in New Zealand".
Dressed in a maroon jersey and jeans, the man stood silently in the dock throughout the hearing.
He did not apply for bail and will stay in custody until later this month.
The blackmail charges are punishable by up to 14 years' jail.
Massey University's Associate Professor in marketing Henry Chung said yesterday's arrest had given Chinese consumers confidence in New Zealand products and legal system.
He said in China many cases get lost in the system.
Chung said this prosecution had established Chinese consumers trust in New Zealand's legal system.
The Government is also confident we haven't suffered any major damage to our international reputation, following the scare.
Primary Industries Minister Nathan Guy said there was a lot of concern overseas, but he was confident the Government managed to plug any damage.
He said they had kept in touch with all of the interested parties, and the extra testing regime helped calm any fears.
Timeline
Nov 27, 2014: Fonterra and Federated Farmers receive a letter threatening to contaminate infant formula.
Jan 15, 2015: Milk testing methods validated and sampling strategy approved.
Feb 10: First meetings with affected manufacturers.
Feb 11: Initial meetings with major global suppliers.
Feb 13: Food and Grocery Council chief executive told of the threat.
Feb 18: Initial meetings with New Zealand supermarket chains.
Feb 25: Labour leader advised.
March 10: Public informed.
