The men were volunteers with 2nd Battalion The York and Lancaster Regiment and were killed in battle with German troops near the castle of Flandres de Beaucamps-Ligny on October 18, 1914.
Their remains were found during construction work near the village of Beaucamps-Ligny in 2009, and have finally been identified after the authorities matched their DNA with surviving relatives.
The remains of five more soldiers uncovered during the dig have yet to be identified, but the MoD said this work would continue.
Commodore Ian Bisson, from the MoD's Joint Casualty and Compassionate Centre, said it had been a "difficult but very successful" project.
"We have identified far more of the fallen than we first hoped," he said in a statement.
"We can still identify some of the remaining five sets of remains and would appeal to those who think they may be family members to get in touch with us."
Of the 10 soldiers identified nine have surviving family members living in England, while one, Private Leonard Arthur Morley, has relatives in Canada.
They will all be re-buried with full military honours.
At the time of the discovery, local mayor Frederic Motte told AFP that builders hit a skull as they were clearing space for a sewage treatment plant in a new social housing project.
"We alerted the police and the prosecutor's office, then digging a little further we came upon military gear, such as bullets and bandoliers," he said.
"We could see they were British soldiers by their buttons, which had the initials of their regiment," said the mayor, who learned the history of the York and Lancasters after he found a body in his own garden in 2006.
Some of the dead appeared to have been caught by surprise at the moment of their death, he said, while one had a canteen in one hand and a pipe in the other.