Higginson, who is also currently chairman of home shopping group N Brown, joined Morrisons in 2014 to lead a shake-up at the supermarket following years of worsening sales.
He previously spent 15 years on the board at Tesco, with 11 as finance director then four as chairman of Tesco Bank, before quitting in 2011 after being passed over for the chief executive post.
Before joining Tesco in 1997, Higginson was a finance director at high street retailers Laura Ashley and The Burton Group, having started his career at Unilever.
He is currently a non-executive director of retailer Woolworths in South Africa and an adviser to private equity firm Warburg Pincus.
Shore Capital Markets chief executive, Simon Fine, said: “Andy is an exceptionally talented executive with an outstanding consumer industries reputation. We are delighted to have gained his services and we look forward to working together.”
Higginson added: “I have known Shore Capital for many years and enjoy the Group’s entrepreneurial spirit and commercial approach; and am excited about the prospect of helping Shore Capital to further build upon what has been an impressive track record to date.”