More than 4,000 British soldiers were killed every day during the battle
The bodies of the three were among 27 discovered last year by French archaeologists at the site of the Battle of Arras in Northern France.
The Duke of Kent, Armed Forces Minister Dr John Reid and the British Ambassador to France Sir Michael Jay are among the dignitaries attending the ceremony at the British Military Cemetery in Monchy le Preux near Arras.
The bodies of Private Frank King and Private George Hamilton Anderson, who fought with the 13th Battalion Royal Fusiliers were being buried with full military honours.
Private King was just 28 and Private Anderson 32 when they died in battle. A third, unidentified soldier is also being buried at the cemetery. All the other unidentified bodies discovered at the site have already been given full military burials in the same cemetery.
Also attending the ceremony is 98-year-old Harry Wells, who fought at Arras and is one of the few remaining survivors.
A bloody battle
The soldiers were killed in the Battle of Arras, which took place over four days in April 1917.
When the bodies of 27 soldiers were discovered close to the village of Monchy Le Preux near Arras last year, historians said it was one of the largest finds of First World War dead.
The shallow mass grave was found by French archaeologists and is believed to have been the site of a frontline field hospital.
The Battle of Arras was one of the bloodiest of the war - British and German soldiers fought hand-to-hand for possession of the village and tens of thousands died.
Although the Allies claimed victory at the time, historians now say that despite heavy losses they failed to make the breakthrough they hoped for.
Most of the bodies could not be identified but dog tags meant that two of the men being buried on Wednesday have been named.
The British Military Cemetery in Arras, where the soldiers are being buried, is managed by the Commonwealth War Graves Commission which maintains burial sites in 134 countries around the world.