The deal, now awaiting final endorsement by the European Commission, sets down several safeguards and practices to be followed by New Zealand after an outbreak is discovered.
It is hoped the agreement will prevent major trade disruption if a serious disease, such as Foot and Mouth (FMD), is discovered in New Zealand herds.
Measures in the deal include assurances from New Zealand that all dairy exports would be heat treated and that animal products would kept separate from other food exports.
New Zealand is a major dairy exporter to the UK, largely through the Anchor butter brand.
The new conditions would become effective from the moment official notification of a serious animal disease outbreak was given. Current strategy would automatically halt exports indefinitely.
"Despite our geographical isolation New Zealand always has to be on guard against the possibility that a serious and costly animal health disease, such as FMD, could happen here," said Andrew McKenzie, executive director of the New Zealand Food Safety Authority (NZFSA).
"The agreement provides an international model for managing in a proportionate and scientific way what could be serious problems affecting our agriculture trade."
Losses from an FMD outbreak in New Zealand could reach $6bn in the first year, rising to $10bn in the second, according to conservative estimates from the New Zealand government.
An FMD outbreak in the UK in 2001 saw five million sheep, 764,000 cattle and 435,000 pigs and goats slaughtered. Compensation paid to farmers hit $6bn, estimated losses via reduced tourism were $15bn.