Gibson, who is former deputy chairman of Asda, will take up his role on September 1.
Sir Ken Morrison has informed the board that he will step down as chairman of the company no later than March 13, 2008 when Gibson will become non-executive chairman of the grocer.
Sir Ken Morrison said: 'Sir Ian Gibson's combination of retail sector and strategic board experience will no doubt be vital at this important stage in the company's evolution and I am delighted that he has decided to join the Morrison's team.'
'With Ian's appointment we will have an excellent board in place and I am confident that the group will continue to deliver value for all stakeholders.'
Gibson said: 'This is a great opportunity for me to work with one of the UK's leading companies and I am looking forward to being part of the dynamic and challenging supermarket sector once more.'
Gibson holds a number of non-executive positions including chairman of Trinity Mirror, director for Greggs, GKN and Northern Rock.