Hundreds of people took flowers to Finsbury Park and gathered outside a mosque in the area on Monday night at a vigil held for victims of the terrorist attack that took place less than 24 hours earlier.
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.
It is the fourth terror attack in the United Kingdom in recent months, and the third to hit London, following a vehicle being rammed into pedestrians on the bridge next to the Houses of Parliament, the concert bombing in Manchester, and the attack on London Bridge and Exmouth Market in which two Australians were among those who lost their lives and in which terrorists also used a van to mow innocent people down.
The attack, which followed three Islamic State group-inspired attacks in Britain, drew criticism from the Muslim community, which said police were slow to call the incident a "terror attack".
Police said inquiries were still ongoing to establish whether the man died as a result of the attack.
One man also died after slipping outside the Muslim Welfare House as evening prayers concluded for the holy month of Ramadan.
The van was apparently driven at people who were helping him.
Incredible messages of strength and unity have flooded Finsbury Park after an a terror attack outside a mosque. "I saw him on the news and I thought "oh my God" that is my neighbour".More news: Wenger speaks to Mbappé about move to Arsenal
In a statement on behalf of the family, Osborne's nephew, Ellis Osborne, said they were devastated for the families of the victims but said that his uncle was not a racist.
Police, who haven't formally named him, said Tuesday they could not release details on whether the attacker was drunk at the time of the attack or whether he was on other medication.
According to witnesses from the scene, the driver drove his van towards the Finsbury Park mosque yelling, "I want to kill all Muslims!"
Pub regular Phil Henry said Osborne was kicked out of the Hollybush pub on Saturday after shouting about Islam.
Khadijeh Sherizi said Mr Osborne was polite and her children, who are Muslim, would play with his children most days. I know him. I've lived here for five years, he was already living here when I moved in. "I am a Muslim".
Describing it as "every mother's worst nightmare", she told The Sun: "My son is no terrorist - he's just a man with problems and I don't know how to cope with all this".
Another resident said Mr Osborne was a friendly neighbour, helping her lift heavy items and always playing with his children in the park.
Faith leaders were joined by Metropolitan Police Commissioner Cressida Dick at the vigil, which started with a short silence.