Soames, grandson of former British Prime Minister Winston Churchill, was former chief executive officer at British outsourcing company Serco Group until September.
Soames will be appointed as an independent non-executive director at the company's annual general meeting on April 26 and will succeed as chair from Sept. 15, Smith+Nephew said in a statement.
His appointment as independent non-executive director is subject to shareholder approval, it added.
Quarta will continue as chair to ensure a smooth transition, and will put himself forward for re-election as a non-executive director.
(Reporting by Radhika Anilkumar in Bengaluru; Editing by Rashmi Aich)