O’Dwyer will be joining Capability following a career in the voluntary, NHS and local government sectors.
She is currently chief executive of the Mungo Foundation, the large social care charity in the West of Scotland.
Previously, she worked as an assistant director of planning and community care with Greater Glasgow Health Board and worked for two local authorities and a homeless charity.
Speaking about her new post, which she will take up in November,
O’Dwyer said: “I look forward to leading Capability into the future and, with everyone who is part of the organisation, taking on the challenges we will undoubtedly face.
“I have already been impressed by Capability’s commitment to placing the customer at the heart of the organisation, whether it is in recruitment, developing and delivering quality services or campaigning for changes that will make a real and positive impact to the lives of disabled people.”
O’Dwyer will replace Alan Dickson, who is retiring after 14 years leading the disability charity.