Analysts welcomed the appointment of Mr Higginson, who will take over on October 1 following the retirement of Sir Ian Gibson, but retail expert Nick Bubb suggested it spelt an uncertain future for Mr Philips.
Mr Bubb said the embattled chief executive could "sleep easy for a couple more months" before the new chairman takes up his role, but added: "After that the pressure will be on and it will be interesting to see how long he lasts."
Mr Higginson spent 15 years on the Tesco board, including as finance director and chief executive of retailing services - overseeing its online and bank divisions - before leaving in 2012
He is currently chairman of 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% fall - as the supermarket sector faces a squeeze from discounters Aldi and Lidl.
It plunged to an annual loss of £176 million 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 £1 billion 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.