The defender, who was Phil Brown's first signing at the club, was informed of his manager's decision on Wednesday at their summer training camp in Madrid.
"I'm honoured to have been chosen by the manager to wear the armband, it was a fantastic feeling when he told me this morning," White told the club's official website.
"Hopefully I can lead the club into a very good and successful season on the pitch."
Brown added: "John leads by example both on and off the pitch, he has a fantastic work rate and is a real professional.
"Without jinxing anything I hope he'll be able to play in every game next year, there's a real consistency to his performances.
"I had five or six candidates to be honest but I've gone with John and I'm sure he'll do an excellent job."