The remains of the 13 men, three women, two children and seven unidentifiable bones hit by the plague were discovered in the capital during the last year.
The skeletons were found under Farringdon's Charterhouse Square during excavation work for the £14.8billion project.
Experts called the discovery "significant" and said thousands more bodies could be buried at a mass grave in the area that was then outside the city limits.
Historical documents suggest the burial ground was established for poor strangers
Jay Carver, Crossrail's lead archaeologist, said: "This is probably the first time in modern archaeological investigation that we have finally found evidence for a burial ground in this area which potentially contains thousands of victims from the Black Death and potentially later plague events as well.
"Historical documents suggest the burial ground was established for poor strangers.
"There is no doubt from the osteological work that the individuals buried here were not the wealthy classes, and they are representing the typical Londoner."
Experts said the discovery provided the first evidence of the location of the second emergency burial ground set up in the capital.
The burial ground had been referenced in historical documents but until now it had never been found.
Mr Carver added: "Analysis of the Crossrail find has revealed an extraordinary amount of information allowing us to solve a 660-year mystery.
"This discovery is a hugely important step forward in documenting and understanding Europe's most devastating pandemic."
The Black Death spread from Europe to England in 1348 and the bodies are estimated to have been buried between 1348 and 1349.
DNA analysis revealed that four of the people had remnants of the Yersinia pestis bacteria on their teeth - which causes the bubonic plague.
Experts said that all of the signs point to the site being used as a Black Death burial ground.
Osteologist Don Walker, from the Museum of London Archaeology (Mola), said he was "amazed" how much information could be gleaned about each person.
He said: "The skeletons discovered at Crossrail's Farringdon site provide a rare opportunity for us to study the medieval population of London that experienced the Black Death.
"We can start to answer questions like: where did they come from and what were their lives like? What's more, it allows for detailed analysis of the pathogen, helping to characterise the history and evolution of this devastating pandemic."