"We will discuss the situation in Zimbabwe, including work on a new constitution and the outlook for the next elections. The visit will also allow us to consider how we might rebuild the bilateral relationship, in the right political environment."
New Zealand imposed bilateral sanctions on Zimbabwe in protest at the Mugabe regime's human rights abuses in 2002.
Mr Tsvangirai is the first member of the Zimbabwean Government to make a formal visit to New Zealand for more than a decade.
He will meet Mr Key and other senior ministers on Wednesday.