After scrutinising the handwriting, they found the copies held in Lincoln and Salisbury were written by scribes based at those cathedrals, rather than by someone working for King John, who ruled England from 1199 to 1216.
The new discovery sheds further light on the Church's role in the creation and distribution of Magna Carta - which sought to restrain the powers of the king.
Lead investigator Professor Nicholas Vincent, said to identify the authors was a "significant achievement".
"It has become apparent, not least as a result of work undertaken for the Magna Carta Project, that the bishops of England were crucial to both the publication and the preservation of Magna Carta.
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"King John had no real intention that the charter be either publicised or enforced. It was the bishops instead who insisted that it be distributed to the country at large and thereafter who preserved it in their cathedral archives," Vincent was quoted as saying by the BBC.
The project, involving academics from the University of East Anglia and King's College London, found the Lincoln Magna Carta was written by a scribe who produced several other documents for the Bishop of Lincoln and Salisbury's was "probably" made by someone working for the cathedral's dean and chapter.
"This overturns the old view that the charters were sent to the sheriffs in charge of the counties. That would have been fatal since the sheriffs were the very people under attack in the charter.
"They would have quickly consigned Magna Carta to their castle furnaces," Carpenter said.
Magna Carta, signed by King John 800 years ago, laid the groundwork for the modern state, imposing the first limits on the monarch's power.
The Royal Barge Gloriana is leading 200 boats from Hurley in Berkshire to Runnymede in Surrey, where the document was signed, over two days.