It's a debate that has long divided motorsport fans but one that the UK-based university believes it has found the answer to.
After racking up five world championship wins between 1951 and 1957, Fangio is ranked top of the podium by the study, which was based on a driver's talent rather than their car.
The Argentine, who graced F1 circuits in the sport's early days, beat off competition from second-placed Alain Prost and Fernando Alonso in third, while legendary Brazilian drive Ayrton Senna, who was killed in an accident during the San Marino Grand Prix in 1994, ranked fifth.
Fangio won the world championship with four different teams -- a record still not matched today -- while he also remains the oldest world champion, having taken the 1957 title aged 46 years and 41 days.
"The question 'who is the greatest Formula One driver of all time' is a difficult one to answer, because we don't know the extent to which drivers do well because of their talent or because they are driving a good car," Dr Andrew Bell said.
"Our statistical model allows us to find a ranking and assess the relative importance of team and driver effects."
Bell concedes it was difficult to take into account changes in racing technology over time, but said the research showed that, as the years have gone by, the team rather than the driver is a great indicator of success.
The study found that teams matter around six times more than drivers when it comes to taking the checkered flag in F1.
"It's obviously a difficult thing to compare, different drivers from different years -- if you put Fangio in a modern-day car he probably wouldn't do very well, and similarly the other way round," Bell told CNN.
"So we looked at how much these things change over time. The team matter significantly more, the model says, and that has increased over time.
"As time has gone by, the performance of the car has mattered more and the importance of the driver has mattered less."
While Michael Schumacher is the most successful driver with seven world championships and an unparalleled 91 race wins, people may be surprised by his ranking in the study, which has been published in the Journal of Quantitative Analysis in Sports.
The German only sits in ninth spot once his team's impact is removed, with his post-retirement performances with Mercedes from 2010 to 2012 dragging him down.
Schumacher, who also raced for Ferrari, Benetton and Jordan, would actually rank third in the study if only his pre-retirement career was taken into account.
Three-time world champion Niki Lauda, meanwhile, fails to even make the university's top 100 chart, with relatively unknown Christian Fittipaldi, without a world title to his name, making the top 20.
"Our statistical model [provides us] with some surprising results," Bell said. "Had these drivers raced for different teams, their legacies might have been rather different."
"When Lauda was performing at his best he was at Ferrari, which is a very higly-ranked team. When he moved teams, his actual performance dropped, which came out in the model," Bell added.
"Fittipaldi came out as one of the best drivers, which at first you think must be a mistake, but actually the model can bring out performances of drivers who might not win championships and are in low quality cars.
"The key thing was he was able to keep his car on the road, when his teammate wasn't, which helped very much in his favor in this model.
"When you take out the team effect you're seeing how well you compare to your teammate.
"So if you win lots of championships but your teammate comes second, that won't count in your favor. Where as if you beat a teammate much more significantly that suggests it's down to your driving rather than the car."
While Schumacher's ranking and Fittipaldi's inclusion ahead of Lauda will be sure to raise eyebrows, Bell believes that in Fangio the study has found a worthy winner.
"He dominated the early 50s and he would firmly have a right to be up there, so I don't see any reason why he can't be number one," Bell said.
"The question 'who is the greatest Formula One driver of all time' has fascinated fans for years and I'm sure will continue to do so."
University of Sheffield study's top five F1 drivers of all time:
1. Juan Manuel Fangio (ARG)
2. Alain Prost (FRA)
3. Fernando Alonso (SPA)
4. Jim Clark (SCO)
5. Ayrton Senna (BRA)