Darren Osborne, a 47-year-old who is believed to be a father-of-four from Cardiff, was arrested after pedestrians were targeted by a man driving a van near Finsbury Park Mosque in north London early on Monday.
In a statement on behalf of the family, Osborne’s nephew Ellis Osborne, 26, said: “We are massively shocked; it’s unbelievable, it still hasn’t really sunk in.
“We are devastated for the families, our hearts go out to the people who have been injured.”
Mr Osborne added his uncle was “not a racist” and said he had never expressed any racist views.
He added: “Its madness. It is obviously sheer madness.”
The London Ambulance Service took nine people to three London hospitals. Two others were treated for minor injuries at the scene.
Witnesses described hearing a van driver, who was detained by members of the public at the scene, shout: “I’m going to kill Muslims.”
The man was initially arrested on suspicion of attempted murder but Scotland Yard said he was later arrested for the commission, preparation or instigation of terrorism including murder and attempted murder.
Residents near Cardiff said they were “shocked” after seeing photographs of their neighbour being arrested in London.
In a telephone interview with ITV News, his mother described him as a “complex” person but said “that’s all I can say”.
The woman, who is not being named, broke down in tears.
She said: “It’s a terrible, terrible shock.”
Police have been searching a residential address in Pentwyn, where Osborne is listed as living.
Five residents identified images of the man being arrested as their neighbour, Osborne, who according to reports is originally from Somerset.
Neighbour Khadijeh Sherizi said: “I saw him on the news and I thought ‘oh my God’ that is my neighbour.
“He has been so normal. He was in his kitchen yesterday afternoon singing with his kids.
“He was the dad of the family. He has kids. He lives next door. He seemed polite and pleasant to me.
“I just can’t believe it.”
Scotland Yard said the attack unfolded while a man who had taken ill was receiving first aid from the public.
He was pronounced dead at the scene at 1:04am.
A spokesman said police investigations are “continuing to establish whether there is any link between his death and the attack” adding: “The man suspected of driving the van was detained by members of the public at the scene.”
Imam Mohammed Mahmoud was hailed for his efforts to prevent a mob attack and calm the situation before police arrived in shielding the suspected terrorist from the fury of onlookers.
He said: “By God’s grace we managed to surround him and protect him from any harm.
“We stopped all forms of attack and abuse towards him that were coming from every angle.”
Deputy Assistant Commissioner Neil Basu said it is being “treated as a terrorist incident” adding: “The investigation is ongoing and we are working fast to know the full details of how and why this took place.
“All the victims were from the Muslim community and we will be deploying extra police patrols to reassure the public, especially those observing Ramadan.”
The suspect, who is believed to have been from Weston-super-Mare, remains in custody at a south London police station.
The attacker, who is believed to have acted alone, struck as the area was busy with worshippers attending Ramadan night prayers at the mosque.
Eight people were taken to hospital, with one since discharged, while two others were treated at the scene.
Earlier, Metropolitan Police Commissioner Cressida Dick said the incident was “quite clearly an attack on Muslims” and that “we treat this as a terrorist attack”.
She said: “Sadly we have suffered a number of attacks and very sad events over the last few weeks.”
Security Minister Ben Wallace confirmed the suspect was not known to the security services.
He told BBC Radio 4’s World At One: “What I can say on this case is this individual, so far as we know at the moment, was not known to us, but we are aware of a rise in the far right.”
Prime Minister Theresa May condemned the incident as “every bit as sickening” as the recent atrocities in London and Manchester.
Witnesses said the suspect was smiling and waving as he brought carnage to Seven Sisters Road, with video posted online showing him give a nonchalant wave as police put him in the back of their vehicle.
Images of the van showed it was rented from Pontyclun Van Hire in Pontyclun, near Cardiff.
Flowers have been laid near the scene, with one card reading: ‘’This is an attack on all Londoners and on my community.’’
Another read: ‘’I was so sorry to hear the news this morning. #NotInMyName’’.
Scotland Yard said detectives currently believe the attacker “acted alone but we are of course investigating all the circumstances leading up to the attack”.