They were strongly opposed by Opposition political parties and teaching unions, but were implemented as part of the National Party's confidence and supply agreement with Act.
"As is the case with all partnership schools, learning outcomes will be closely monitored by the Ministry of Education and the Partnership School Authorisation Board, and reported on publicly," Mr Seymour said.
"This ensures strong accountability to the communities these schools serve.
"The exact number of new schools to open will depend on the quality of the proposals received."
Eight charter schools are currently open.
One of the first charter schools, Te Pumanawa o te Wairua, at Whangaruru in Northland, was terminated last year. It was closed due to concerns about poor teaching, low achievement and an inadequate curriculum, and in total cost around $5 million
It has also been announced an independent Partnership School support entity, E Tipu E Rea, has been established to support new, existing, and prospective charter school sponsors and will receive a conditional funding grant.
Mr Seymour said this would bring New Zealand into line with international charter school models.
"England has the New Schools Network, New York has the New York Charter School Centre, and New Zealand now has E Tipu E Rea.
"E Tipu E Rea will join other independent entities such as the New Zealand School Trustees Association in providing support services to the New Zealand school system. It will seek most of its funding from private sources."
The Board will be chaired by former CEO of EY Australasia Rob McLeod.