Darren Osborne was found guilty of murdering 51-year-old Makram Ali and trying to kill others in the Finsbury Park area of north London in the June 19 attack.
A Briton who deliberately drove a van into a group of worshippers near a London mosque, killing one man, was on Friday sentenced to life in prison with a minimum 43-year term.
Darren Osborne, 48, from the Welsh capital Cardiff, was found guilty of murdering 51-year-old Makram Ali and trying to kill others in the Finsbury Park area of north London in the June 19 attack.
Passing sentence at a London court, judge Bobbie Cheema-Grubb told Osborne: "This was a terrorist attack. You intended to kill."
She added that he had been "rapidly radicalised" and that his "mindset became one of malevolent hatred".
"In short you allowed your mind to be poisoned by those who claimed to be leaders."
The unemployed "loner" had pleaded not guilty, telling the court that a man called "Dave" was driving at the time - a claim police denounced as a fabrication.
The May Manchester suicide bombing and the June London Bridge van attack and stabbing rampage further fuelled his obsession.
Witnesses recalled Osborne saying: "I've done my job, you can kill me now" and "at least I had a proper go" in the immediate aftermath of the attack.
After two weeks of evidence, the jury took one hour on Thursday to find him guilty.
Osborne had watched a BBC television drama which told the story of three victims of the child abuse ring, and quickly grew angry at what he deemed as inaction over the scandal, the court heard.
Osborne began researching far-right material online, police said.
He then hired a van and drove to London intent on ploughing into a pro-Palestinian march, but was prevented from doing so by road closures.
Osborne then drove around London looking for a target before heading to Finsbury Park, where worshippers were leaving a mosque and an Islamic centre after Ramadan evening prayers.