Zack Davies, 26, targeted Dr Sarandev Bhambra at a Tesco store in Mold, Flintshire, in a racially motivated revenge assault for the murder of Fusilier Lee Rigby.
Davies, of Mold, admitted wounding with intent but denied attempted murder.
He was convicted at Mold Crown Court on Thursday.
He will be sentenced on 11 September.
Dr Bhambra was walking down an aisle in the store on 14 January when he felt a "huge blow" to the back of his head from the 30cm (12in) machete.
During the trial, shopper Leanne Jones said she heard the words "white power" and said Davies was acting "like a lunatic" as he hacked Dr Bhambra with the machete.
Another witness heard Davies say: "Come here, this is for Lee Rigby".
Dr Bhambra suffered two cuts to his scalp which went down to the bone and a cut to his back which went down to the muscle.
The injury to his left hand caused major nerve, artery and tendon damage and he was in surgery for five hours.
Dr Bhambra told the jury that former soldier Peter Fuller saved his life when he intervened during the attack.
The court heard items associated with white supremacy and Nazism were found at Davies's home, including banners, swastika badges and Combat 18 stickers.
He also said he was "absolutely fascinated" with Islamic State and described the British man known as Jihadi John as his inspiration.
Gareth Preston, senior prosecutor for the Crown Prosecution Service Wales, described Davies as a "dangerous young man whose distorted and racist views led him to commit a terrifying act of violence".
He added: "Such was the level of violence involved that, were it not for the extremely courageous actions of ex-serviceman Peter Fuller, this offence could have become an act of murder."
Michael Adebolajo and Michael Adebowale were jailed for life in February 2014 for hacking Fusilier Rigby to death.
A man has been found of guilty of attempted murder after attacking a dentist with a machete and a hammer in north Wales.