Boycott will lead the charity from 7 October, following four years at Shelter as director of campaigns, policy and comms.
She replaces outgoing chief executive Neil Churchill, who has joined the NHS commissioning board as national director of patient experience.
Asthma UK chairman Rob Wilson said: "Kay has the expertise, focus and determination to lead our organisation into a new era in our fight against asthma.
"As we focus on our new strategic goal of preventing asthma attacks that lead to hospitalisation and death, Kay’s leadership skills and impressive marketing and influencing experience will be invaluable."
Before her time at Shelter, Boycott worked in the private sector working in marketing and customer roles with Nestlé Rowntree and Johnson & Johnson. This was followed by ten years in commercial strategy consultancy, with clients including GlaxoSmithKline and Vodafone.
She also spent five years as non-executive director and audit chair of an NHS Primary Care Trust.