Higginson, who is currently chairman of discount retailer Poundland, will join the Tesco board on October 1 2014 as non-executive deputy chairman and chairman elect.
He said he was delighted to be joining the board at Morrisons.
“Whilst there are undoubted challenges in the industry at the moment, this is a fine business and I am looking forward to working with the great team at Morrisons who work hard every day to serve customers,” Higginson added.
He is also currently chairman of the N Brown Group and senior independent director of BSkyB.
Before this, he served as an executive director at Tesco for 15 years.
Gibson, who has held the chairman role since 2008, said: “Higginson has a tremendous reputation and a distinguished career at the forefront of retailing in the UK and I am sure he will be a huge asset to Morrisons.
“I am very pleased to welcome him to the board as deputy chairman and look forward to working with him to ensure a smooth transition to the chairman role.”
Higginson started his career at Unilever and held executive positions at Guinness Brewing, Laura Ashley and Burton Group.
In 1997 he moved to Tesco, initially as finance director before adding responsibility for group strategy and becoming chairman of Tesco personal finance in 2004.
In 2008 he was appointed ceo of Tesco’s retailing service business, before leaving the business in 2012.
He is also a non-executive director of the Rugby Football Union and of South African-based retail group Woolworth Holdings. His previous non-executive directorship roles include with FirstGroup and Clarks.
Earlier this year, Morrisons revealed plans to cut 2,600 jobs in a management structure.
Former chairman of the retailer Ken Morrison described the recovery strategy of current boss Dalton Philips as “bullshit”.
Philips has also been criticised by some City analysts for allegedly adopting the wrong business strategy, with an over reliance on in-house food manufacturing.