Vigar suffered a head injury in Chichester's non-league match against Wingate & Finchley on Saturday, which was suspended as a result of the incident.
He was placed in an induced coma and underwent surgery in hopes of supporting his recovery, but sadly his injuries were too severe.
Chichester have since released a statement confirming Vigar’s passing, saying: "It is with great sadness that Chichester City Football Club has to confirm the passing of Billy Vigar. Below is a statement from his family. We request that his family's privacy is respected at this most difficult time," the club said.
"After sustaining a significant brain injury last Saturday, Billy Vigar was put in an induced coma. On Tuesday he needed an operation to aid any chances of recovery. Although this helped, the injury proved too much for him and he passed away on Thursday (25th) morning.
"The responses to the original update show how much Billy was thought of and loved within the sport. His family are devastated that this has happened whilst he was playing the sport that he loved."