The ceremony at Runnymede in Surrey, close to the River Thames, is where King John of England sealed the original document in 1215.
The charter first protected the rights and freedoms of society as well as establishing that the King was subject to the law rather than being above it.
Prime Minister David Cameron is also attending the event.
He told the audience the document went on to “change the world”.
It would “alter forever the balance of power between the governed and the government”, the prime minister said.
Mr Cameron added the document had inspired countries across the world.
He said: “Why do people set such store by Magna Carta?
“Because they look to history. They see how the great charter shaped the world, for the best part of a millennium, helping to promote arguments for justice and for freedom.”
Earlier, the Duke of Cambridge was shown a new art installation commissioned for the anniversary.
The work, called The Jurors, is inspired by the 39th clause of Magna Carta, which gives the right to a jury trial.
Artist Hew Locke said it was a “great honour” to be chosen to produce the piece.
There will also be a rededication of the American Bar Association’s Magna Carta Memorial.
A replica of the Great Charter began its journey down the Thames on Saturday as part of the commemorations.
The Royal Barge Gloriana has led 200 boats from Hurley in Berkshire and is due to arrive at Runnymede on Monday.
There are just four known copies of the original Magna Carta in existence today, from an estimated 13 that were made.
Two are held by the British Library, with Salisbury Cathedral and Lincoln Cathedral holding the others.