Woolnough, who is executive director of policy and information at Cancer Research UK, will succeed Kay Boycott in December.
Asthma UK and the British Lung Foundation merged in January, although they maintain separate identities.
Boycott was the chief executive of Asthma UK before the merger and has led the combined charity since. She will move on to a “long-planned portfolio career”, the charity said in a statement.
Woolnough, who has led policy at CRUK since 2005, has previously served as a senior policy advisor at the Department of Health and Social Care and as a policy officer at the Sport and Recreation Alliance.
She is also a trustee of MQ: Transforming Mental Health and the National Cancer Research Institute, and has previously sat on the boards of the premature baby charity Bliss, the Association of Medical Research Charities and Action on Smoking and Health (UK).
Woolnough said in a statement that it was an honour to have been appointed to the new role.
“Respiratory health is a cause I care deeply about, and it’s been inspiring to see the extraordinary lengths that they’ve gone to in supporting people with lung conditions over many years, and most recently during the Covid-19 pandemic,” she added.
Boycott said it had been a privilege to have been chief executive of Asthma UK and then the combined charity.
“I’m extremely proud of what we’ve managed to achieve together, including proving the value of the merger,” she said.
“Leaving such a dedicated and committed team will be a big wrench, but I’m thrilled to be handing over to a leader of Sarah’s calibre.”
Baroness Tessa Blackstone, chair of the combined charities, said she greatly looked forward to working with Woolnough.