Bush revealed that police believe Tarrant is responsible for both attacks.
He said Tarrant did not give up willingly when he was found.
Bush was listening to live audio of the arrest and said Tarrant was "non compliant".
He was arrested 36 minutes after the initial attack at the Al Noor Mosque.
Tarrant is likely to face further charges but Bush could not say what they might be.
"What charges he faces will be determined by the investigation," he said.
Bush acknowledged the bravery of the staff who arrested Tarrant, and other front line officer.
He also thanked other first responders and support agencies including St John, Fire and Emergency NZ, Victim Support, Civil Defence and the Defence Force.
He said some responders and members of the public had shown "absolute bravery" and put themselves in harm's way — action that would have "saved lives".
Bush confirmed the youngest victim of the massacre was a child however he was reluctant to give a specific age range as details of the dead were still being confirmed.
The death toll could still rise.
The Herald is aware of one man in a critical condition who is undergoing a six-and-a-half hour surgery this afternoon.
It is understood he was hit by multiple bullets.
Two other people were arrested and may face charges in relation to the massacre.
Bush said they were still under investigation.
An 18-year-old man has also been charged with inciting racial or ethnic hatred.
Bush said a "considerable" number of people were being looked at as part of the broader investigation including those posting on social media.
He stopped short of saying the teen had been charged due to a social media post — but indicated that was part of the investigation.
He and Canterbury District Commander John Price wanted to reassure the public that there was no "imminent" threat to their safety.
"There is no intelligence about imminent threats," he said.
"But I would never assume anything in this situation.
"We have a number of leads and we are not searching for anyone who is an imminent threat.
"That doesn't mean that doesn't exist."
Tarrant was held in the Christchurch central police station — housed in the Justice Precinct buildings — overnight and walked to the courtroom next door for his appearance.
He said it would be "improper" to confirm this early that there was only one shooter — but it was believed Tarrant was behind all of the terror attacks.
