Lawson will take up her post at Morrisons in September and will serve on the company's management board. She will work closely with interim group HR director Neal Austin in the handover.
Dalton Philips, Morrisons' chief executive, said: "Emily's role will be vital in our transformation of Morrisons into a multi-format, multi-channel retailer."
Lawson said: "I am looking forward to working with colleagues to build an environment where everyone can do their best work, deliver excellent service, and support the communities in which the business operates."