Ms Nolan, who is currently deputy vice- chancellor at Glasgow University, will take up her post on July 1 this year.
She replaces Professor Dame Joan Stringer, who will retire from the role of principal after a decade in the post.
Ms Nolan said: "It is a privilege to lead the university and I look forward very much to working with the university community, to build on the success of Professor Stringer's principalship."
Chairman of Napier's ruling Court, The Very Rev Dr Graham Forbes, welcomed the appointment.
"She was the unanimous choice of our interview panel and is a worthy successor to Professor Dame Joan Stringer," he said.
"We look forward to working with her to ensure the continued growth and success of the university."
Edinburgh Napier has almost 17,500 students, of which around 30% are international students studying either in Edinburgh or undertaking courses delivered with the university's partners overseas.
Ms Nolan graduated as a veterinary surgeon from Trinity College Dublin, Ireland, and after a short time in veterinary practice, embarked on an academic career which took her to the universities of Cambridge, Bristol and the Technical University of Munich.
She was appointed as a lecturer at Glasgow University in 1989 where she established herself as a researcher in the field of animal pain. She was made a professor of veterinary pharmacology in 1998 and took up the post of Dean of the Faculty of Veterinary Medicine a year later.
She became a vice-principal for Learning and Teaching in 2004, and in 2009 was appointed to the position of senior vice-principal and deputy vice-chancellor.
She is a Fellow of the Royal Society of Edinburgh.