The Harry Potter author donated £10 million to establish the centre, now named the Anne Rowling Clinic, which is based at Edinburgh University.
The clinic focuses on research, targeting discovery of treatments that will slow progression of neurodegenerative diseases, with the ultimate ambition of repairing damage.
Ms Rowling said: "I am moved and elated to see the Anne Rowling Clinic formally opened today by HRH The Princess Royal.
"Having observed the plans for the Clinic develop and expand to fulfil the needs of patients, clinicians and researchers, I am now very proud to see the building finished and operating as the beating heart of this centre for excellence. Thank you to everyone who has been involved in its creation and operation."