The agreement will now have to make its way through the British and New Zealand Parliaments before it is able to enter into force. Both sides hope this can happen by the end of the year.
On the British side, New Zealand's free trade agreement will be grouped with Australia's recently concluded free trade agreement and both will be put through Parliament at the same time.
"Essentially the Australia and New Zealand agreements will go together - through our Parliamentary process and through that scrutiny process," Clarke
"Our new Trade and Agriculture committee will look at that as well," she said.
There has already been some anxiety about the agreement expressed by British farmers, who worry about the level of access granted to New Zealand producers. This is despite the fact that in most instances, this level of access is phased in very slowly.
The UK's National Farmers' Union President Minette Batters criticised the signing of the agreement overnight, saying that "in time there will be no limit to the amount of goods New Zealand can export to the UK".
Clarke said there were "safeguards" in the agreement.
"What we've done in terms of the bilateral safeguards - the phasing out of tariffs should give comfort to our agricultural sector," Clarke said.
The UK's eyes now turn to its place in the Comprehensive and Progressive Trans-Pacific Partnership, which it is currently in the process of joining.
New Zealand has so far backed that process. On February 18, the UK was allowed to begin the next phase of joining that agreement, by submitting its market access offer to the group.
Clarke said accession looked positive.
"Our assessment - and I would say its New Zealand's assessment as well - is that it's all looking really good for UK accession, but of course you don't want to short-cut the process in any way - you want to go through properly, make sure you maintain those really high standards to which we all aspire to," Clarke said.
She said the agreement was part of the UK's efforts to engage "much more in this Indo-Pacific region," by strengthening economic and security relationships in the region.