Vigar was a graduate of the Arsenal academy and also had spells at Derby County, Hastings United and Eastbourne Borough.
Derby County said in a statement: “All at Derby County are deeply saddened by the passing of Billy Vigar.
“Billy spent the second half of the 2022-23 season with the academy on loan from Arsenal, making several appearances for the Under-21s.
“The thoughts of everyone at the club are with his family and friends at this incredibly difficult time.”
A spokesperson for Hastings said: “All of us at Hastings United are devastated to learn of the passing of Billy Vigar.
“We will always remember Billy’s time at Hastings United with fondness. Our thoughts are with Billy’s family [and] friends at this time.”
Vigar made 32 appearances for Eastbourne while on loan from Arsenal during the 2023-24 season.
Eastbourne said: “[We] are devastated to learn of the passing of former player Billy Vigar.
“Both footballing and non-footballing club staff are shocked and deeply saddened of the news, and our thoughts are with Billy’s family at this terrible time.”
The FA said in a statement: “We send our heartfelt condolences to his family, friends, loved ones and everyone at Chichester City FC at this incredibly difficult time.”
Chichester confirmed on Thursday morning, before announcing Vigar had died, that their match against Lewes on Saturday was postponed and would be rescheduled at a later date.