Gary MacDonald Graham, 57, from Borras, Wrexham, had been walking on the A534 at Llan-y-Pwll link road, which serves Wrexham Industrial Estate.
The road remained closed on Friday following the incident on Thursday night.
Mr Graham's family said: "He was a beloved father, brother, grandfather, uncle and friend."
They added he would be "sorely missed by all who knew him. He is reunited at last with his wife, Sian Graham, who was his first love."
Mr Graham was a former member of the 2nd Battalion Scots Guards who fought at the battle of Tumbledown during the Falklands War.
Police said he had been walking between Holt Road roundabout and Wrexham Industrial Estate roundabout near to Wrexham Golf Club just after midnight when he was hit. The vehicle did not stop.
Officers have appealed for witnesses to the collision and advised motorists to avoid the area on Friday.
Ch Insp Darren Wareing said: "I am appealing for the driver of the vehicle involved to come forward.
"I am also appealing for any witnesses who would have been in the area at the time or who may have witnessed the collision to call police."
A Falklands War veteran has been killed after being hit by a car which failed to stop.