French Open runner-up Cobolli was the highest-ranked player the 23-year-old Fery has faced during the tournament, but on a sweltering Centre Court he produced another fearless performance to outclass his opponent.
Fery is the first wildcard to reach the men's singles semi-finals at Wimbledon since Goran Ivanisevic memorably won the title in 2001 and his bid to emulate the big-serving Croat will continue against second seed Alexander Zverev.
"It seems to get better and better every match, I can't believe it," a stunned-looking Fery said on court minutes after ending the contest with an ace.
"That last game I felt emotions that I haven't experienced before in my life."
Arrived as virtual unknown
Born in France to French parents, raised within walking distance of Wimbledon and a graduate of California's Stanford University, Fery arrived at the tournament ranked 114th in the world and largely unknown to the wider British public. His exploits over the past fortnight have changed that.
His victory means he is only the fifth British man in the professional era to reach the Wimbledon semi-finals, joining Andy Murray, Tim Henman, Roger Taylor and Cameron Norrie and he will be the country's new number one next week.
He was applauded by Britain's Queen Camilla from the Royal Box and had been watched by Kate, the Princess of Wales, in an earlier round.
Fery beat a sick Cobolli in the first round of this year's Australian Open - only his second Grand Slam match win after reaching the second round of Wimbledon last year.
But the in-form Italian was expected to provide a reality check to what British media have dubbed the "Fery-tale" for his fairytale run.
Errors flowed off the Cobolli racket
Cobolli had the first chance of the match but failed to convert a break point at 3-3 in the first set and the Italian wavered when serving at 4-5, double-faulting and then missing a forehand to pass up the opening set.
Fery leapt in the air and pumped his fists and the crowd, slowly grilling in the searing heat, roared their approval.
With multi-millionaire father Loic and mum Olivia, a former French player, watching from the stands, Fery recovered from dropping serve early in the second set and piled on the pressure before dominating the tiebreak to put one foot in the semis as errors flowed off the Cobolli racket.
With 14 hours already in his legs just to reach the quarter-finals, including marathon five-set victories in both the previous rounds, Fery showed no sign of fatigue as he broke Cobolli's serve at the start of the third.
Even two-time champion Murray was known to put the home fans through the wringer at Wimbledon, but Fery was not in the mood for extended drama, keeping a stranglehold on an opponent who simply had no answer to Fery's intensity.
Nervous but kept going
Cobolli's last stand was having two break back points in the second game but twice Fery showed incredible resilience and dexterity to fight those off, winning both points with smashes after covering almost every blade of grass.
Fery simply could do no wrong. Even when a Cobolli backhand veered off the net cord and Fery slipped trying to change direction, he still flicked away a winner to reach match point.
After firing down his eighth ace he dropped his racket and then collapsed to the turf in disbelief.
"I played Flavio earlier this year and I beat him in Australia which was a boost of confidence," Fery said. "I was very nervous before but I just kept going until the finish."
The only other men's wildcards to reach Grand Slam semi-finals are Jimmy Connors at the 1991 US Open and Henri Leconte at the 1992 French Open.