Announcing the agreement, President Park made special mention of New Zealand's part in the Korean War, saying it was "a very strong friend, one that fought beside us during the Korean War."
Mr Key said he believed that had been a critical factor. "The President has a genuine affection and belief that New Zealand came to aid of Korea during the Korean War and she believed New Zealand should be repaid for the bravery and courage of those who went to fight in the defence of Korea. I think she was never prepared to leave New Zealand behind given they had signed free trade agreements with Australia and other countries."
Other countries with agreements with Korea include Chile, the European Union, the United States, Canada and Australia.
Mr Key said President Park had provided the necessary leadership to drive the free trade agreement.
Trade Minister Tim Groser said no other country had achieved a better deal and New Zealand had decided the compromise over milk powder was worth it, given the other markets for milk powder. There was also a chance Korea would join the Trans Pacific Partnership in future which would give another chance to see those tariffs removed.
Tariffs on products including infant milk formula and cheese would be eliminated over the next decade. The deal has taken five years to negotiate. Mr Groser said the difficulty in getting an agreement was expected given the protests in Korea over removals of the protections for agriculture.
"Anyone who has followed Korean politics knows that the opposition to agriculture liberalisation is just off the planet .. It's been unbelievably difficult to get this on the right page."
He opted to focus on the positives - saying the deal was good news for kiwifruit and squash exporters.
"We are the largest exporter of squash to Korea, about $17-18 million. I mean, it's not enormous but you can be sure the guys who are producing squash in New Zealand will be pleased to see free trade coming down their way."
Mr Groser said many businesses were on the verge of being forced out of the market because of the tariffs imposed on their goods while other countries did not face the same tariffs. It is the first bilateral trade agreement to be signed by the National Government.
In return for lifting tariffs, New Zealand has agreed to extend schemes such as the Working Holidays and student exchange programmes with Korea. Mr Groser said New Zealand already had next to no tariffs.
• Korea is NZ's 6th largest export destination and 8th largest for imports.
• Total two way trade amounts to $4 billion.
• NZ companies currently pay about $229 million a year in tariffs.
• That will drop by $65 million in the first year of the FTA
• Most remaining tariffs will phase out over 15 years
• Tariffs will stay on milk powder but removed on most other dairy products, including infant milk formula.