English said he expected the legislation to get its next reading in Parliament next month and wanted broad political support for it.
The only minority view in the report was from the Green Party, which said it provided for "new, intrusive powers" it did not believe were justified.
However, Labour's shadow Attorney General David Parker said Labour would support it.
"The Labour Party is supporting it because we believe that this tightens the regulation of the spy agencies whilst enabling them to do what they need to do."
He said the changes meant New Zealanders could not be spied on for political purposes by removing "purpose-based" warrants.
Those allowed agencies to undertake surveillance or intercept communications for a specific purpose but without stating who the people involved were.
Extra controls have also been added where warrants were required simply to test new technology or equipment or to train staff.
There would also be a fixed-term standing authorisation for the spy agencies to get business records from banks and telecommunications companies which were currently voluntarily provided.
It also called for the agencies to get direct access to Police records on people and financial intelligence held by Police.
The changes also see increased oversight of the agencies' work, including extra reporting to ministers and registers for the Inspector-General - such as a register of spies working under assumed identities.
The committee also recommended swifter destruction of irrelevant, unauthorised or incidentally obtained information and removing a clause which allowed changes to be made to the list of Government databases the agencies can access without any parliamentary oversight.
The overhaul was prompted by a review of the GCSB and SIS and their legal powers by Sir Michael Cullen and Dame Patsy Reddy in March 2016. That will see the agencies powers defined under one act, rather than four as at present.
It recommended changes that will amount to a near-merger of the GCSB and SIS - giving the two agencies the same powers and objectives and expanding the GCSB's powers to spy on New Zealanders - while toughening up the warrant regime and oversight to insure those powers were not abused.