Private George William Chafer, who was born in Bradford, delivered a message under bombardment after the original messenger was knocked unconscious.
The VC is the highest military decoration and awarded for valour in the face of the enemy.
A commemorative paving stone has been laid in the city's Norfolk Gardens.
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"For conspicuous bravery during a very heavy hostile bombardment and attack on our trenches, a man carrying an important written message to his company commander was half buried and rendered unconscious by a shell.
"Private Chafer, at once grasping the situation, on his own initiative, took the message from the man's pocket, and, although severely wounded in three places, ran along the ruined parapet under heavy shell and machine gun fire, and just succeeded in delivering it before he collapsed from the effects of his wounds.
"He displayed great initiative and a splendid devotion to duty at a critical moment."
Private Chafer was born in 1894 in Bradford but after his mother died he was raised by his aunt in Rotherham.
He joined the East Yorkshire Regiment in 1915 and was posted to Meaulte, near Albert, in France where he was awarded the VC on 3-4 June 1916.
He survived the conflict but had a false limb fitted after severe leg injuries. He died in Rotherham in 1966.
The stone being laid is part of a national scheme to recognise World War One recipients of the Victoria Cross.
A World War One soldier who was awarded the Victoria Cross (VC) in an outstanding act of bravery has been commemorated 100 years after the event.