Mr Higginson will replace Sir Ian Gibson when he retires in 2015.
Mr Higginson will join the Morrisons board on October 1 as non-executive deputy chairman and chairman elect.
“Mr Philips can sleep easy for a couple more months, but after that the pressure will be on and it will be interesting to see how long he lasts,” said independent retail analyst Nick Bubb.
Bradford-based Morrisons is on a par with Tesco as the worst-performing of the so-called big four grocers, trailing Leeds-based Asda and Sainsbury’s.
Sales fell 3.8 per cent year-on-year in the 12 weeks to July 20 - the same percentage decline as Tesco - while market share dropped to 11 per cent from 11.5 per cent.
Mr Higginson left Tesco in 2012 and was most recently the chairman of Poundland and home shopping group N Brown but stepped down from the chair of Poundland when his new role at Morrisons was announced. Poundland’s senior independent director and former Sainsbury’s finance chief Darren Shapland replaces him.
Mr Higginson said: “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.”
Current chairman Sir Ian Gibson said: “Andy 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.”
Analysts at Shore Capital said: “Mr Higginson brings a wealth of experience and talent to what it has to be said has been a troubled group.”
Mr Higginson joins Morrisons amid a continuing sales slump - with latest quarterly figures showing a 7.1 per cent fall - as the supermarket sector faces a squeeze from discounters Aldi and Lidl.
It plunged to an annual loss of £176m for the year to February 2 and last month announced it was slashing 2,600 jobs as part of a drive to modernise the way its stores are managed.
The Bradford-based firm has said it is investing £1bn over three years as it cuts prices to compete, while it is also belatedly rolling out its online food offer this year, years after its main competitors entered the market.
Chief executive Mr Philips was subjected to a humiliating dressing down at the firm’s AGM last month when former boss Sir Ken Morrison compared his strategy with the manure produced by his cattle herd.