The University of Otago and University of Auckland medical schools had also made a rival joint proposal.
"The Government will now run a contestable business case process to consider all options for delivering the new School of Rural Medicine, and ensure it meets the needs of rural New Zealand," Goldsmith said.
"It is our intention that the successful applicant will be known in 2018 with the new medical school to be up and operating no later than 2020."
The cost of the new school is yet to be finalised, but the Waikato proposal sought about $300 million over 10 years. The Government funding will come through existing tertiary funding streams and future operating and capital budget allowances.
Currently rural and provincial centres rely on about 1100 overseas doctors recruited to work in New Zealand each year.
Responding to the announcement, University of Waikato Vice-Chancellor Professor Neil Quigley said the commitment showed the "extent of the health crisis facing rural and vulnerable New Zealanders".
"Rural and high-needs communities have suffered decades of neglect from the two existing medical schools, so the solution needs to be a fundamental change in the way that we select and prepare medical students for community service."