Both attacks prompted Ardern to condemn the actions of those responsible.
"Our thoughts are with the families of the victims of the attacks," the Prime Minister told the Herald today.
"We condemn all acts of terror and offer our support to the UK Government.
"No matter the place they occur, terror attacks strike at our hearts in the same way."
Meanwhile, Scotland Yard announced 28-year-old Khan as the man behind the attacks in London.
He had previously served time behind bars for terrorism offences and was wearing an electronic tag, according to The Times newspaper.
Khan was also wearing a fake suicide vest when he undertook the attack.
Videos from the scene showed bystanders tackling Khan to the ground, taking his knife and pinning him down before police intervened.
Assistant Commissioner Neil Basu confirmed Khan was shot by police during the incident and died at the scene.
"A number of other people received injuries at this incident," he said, but did not confirm how many.
Basu said a wide cordon was in place for explosives, but "we believe the device that was strapped to the body of the suspect is a hoax explosive".
Those extensive cordons will remain in place for a considerable time," he said.
Witnesses reported hearing multiple shots fired on the bridge on Friday afternoon.
London Bridge was closed to traffic and cars and buses were at a standstill while a white truck lay jackknifed across the stream of traffic.
The incident comes two and a half years after the terrorist attack on London Bridge in June 2017. Eight people were killed and 48 others injured.
Additional reporting news.com.au.