The Royal Barge Gloriana is leading 200 boats from Hurley in Berkshire to Runnymede in Surrey over two days.
Magna Carta was granted by King John on 15 June 1215, establishing that the king was subject to the law rather than being above it.
Twenty-three local people have been chosen as "charter bearers" to relay the document.
The pageant, which started at 09:00 BST, has been organised by Thames Alive, with support from Royal Borough of Windsor and Maidenhead, Runnymede borough and Spelthorne borough councils.
As the copy of Magna Carta is transported downstream, actors will recount its story.
Charter bearers, who live, work or study in one of the three boroughs, will carry the document on board the Royal Shallop Jubilant.
The Queen's Diamond Jubilee barge, Gloriana, is the flagship of the flotilla.
Five-time Olympic gold medallist rower Sir Steve Redgrave, from Marlow, Buckinghamshire, watched as it passed through his home town.
"It's the first row barge that has been built for 300 years so it's pretty spectacular," he said.
The event will culminate with the unveiling of a 4m (13ft) bronze statue of the Queen at Runnymede Pleasure Grounds on Sunday.
Road closures will be in place during the celebrations in Berkshire and Surrey.
The flotilla is due to arrive at Oakley Court Hotel, Windsor, at 20:00. The replica Magna Carta's journey will pause overnight before commencing at 09:00 on Sunday.
Principles set out in Magna Carta charted the right to a fair trial and limits on taxation without representation.
It also inspired a number of other documents, including the US Constitution and the Universal Declaration of Human Rights.
A replica of Magna Carta is being carried down the Thames as part of events to mark its 800th anniversary.