The Great British Menu judge was nominated to support the university's expertise in food and drink and sustainable business, it said.
Ms Leith started the Leith's Good Food catering company and opened Michelin-starred restaurant Leith's in 1969. She has also helped train professional and amateur chefs in her own cook school.
The 76-year-old received an honorary degree from Queen Margaret University in 1997, adding to another 10 honorary degrees or fellowships granted from UK universities.
She will take over the role of chancellor from entrepreneur Sir Tom Farmer, who was installed as the founding chancellor in 2007 when the institution was awarded university status.
Ms Leith said: "Following the wonderful Tom Farmer will not be easy, but I look forward to it.
"I much admire the way QMU has consistently regarded food, nutrition and health as practical and socially important - as well as academic - subjects. I love the enthusiasm and can-do attitude of students.
"I know it will be interesting and fun. I hope I will be useful."
Professor Petra Wend, principal and vice-chancellor of QMU, said: "Prue Leith's career and background resonates deeply with the values and ethos of Queen Margaret University, as well as with our flagships in health and rehabilitation; creativity and culture; and sustainable business.
"She is a highly-respected public figure who has strong beliefs about the importance of education and in its transformational importance to society.
"Much of her life's work has been in food and drink, in which she has shown significant entrepreneurial qualities, but she has also worked hard to help develop and highlight the UK's culinary talent, the importance of good healthy food for all, and to tackle inequalities.
"She is, therefore, an excellent fit for our work in food and drink, which dates back to our inception in 1875 when we were established to help improve the diet of the urban poor."