Johnny Cash site to be preserved
The house in Tennessee burnt down last week, although the cause of the fire has yet to be determined by investigators.
Cash wrote many of his songs at the residence, and played host to a number of notewrothy guests, from fellow musicians to US presidents.
According to the BBC, Gibb said in a statement: "Linda (his wife) and I have decided to build our own home on the higher ground surrounding the Johnny Cash and June Carter Cash home.
"The original foundations shall still be kept intact and preserved for the people of Hendersonville and the people of Nashville."