The Bill was opposed by all opposition parties and the Maori Party.
The Act does not affect the Secret Intelligence Service or the Government Communications Security Bureau which are governed by their own laws.
Chen Palmer senior associate Nicholai Anderson said the legislation was wide-ranging and involved dozens of government agencies.
Under the law, agencies could surveil or search a person if they had reasonable grounds for believing someone had committed, or would commit, an offence, he told TVNZ's Breakfast programme today.
The Government will review the legislation in four years.
Police Assistant Commissioner Malcolm Burgess said the force had rolled out one of its largest training exercises to bring 9000 officers up to speed on the rules.
"What the Search and Surveillance Act does is make clear some of the lack of clarity and it provides some certainty around some of those powers, which is what we want, we don't want to be guessing what our powers are,'' he told RNZ today.
Police could complete some forms of surveillance and searches without warrants, but Mr Burgess said the situations were pretty common sense.
"Either emergencies, where life might be at risk, or where the destruction of evidence might occur in very serious circumstances,'' he said.
"My own interpretation is this is very common sense legislation which provides us reasonable means to carry out our functions.''
He did not see the changes as a massive expansion of police powers.