The band was presented with a team shirt and an early club photograph by the Lord Mayor of Sheffield, Coun Jackie Drayton, after pledging their support to their home city club, which celebrates its 150th anniversary next year.
Sheffield FC is officially recognised by FIFA and the FA as being the oldest football club in the world and already counts Premiership champions Chelsea and England and Yorkshire cricketer Michael Vaughan among its members.
Staff are trying to raise the profile of the grassroots club which has two senior teams, nine junior teams, a women's team and a disability team.
Def Leppard's Joe Elliott said: "The picture is amazing, Sheffield FC should be a national treasure."
Bass player Rick Savage added: "I hope the club gets the recognition it deserves. Sheffield FC is an important part of football history."
Club chairman Richard Tims said: "It was great to talk to the guys. They have been through what we are going through right now – trying to establish ourselves at home and worldwide."