A procession was held at the city centre campus, followed by a ceremony in the university's Saltire Centre.
Prof Yunus was awarded the Nobel Peace Prize in 2006 for his pioneering work with the Grameen Bank, which he established in his native Bangladesh in the 1980s. It is said to have helped lift millions of people out of poverty through its micro-lending system.
His daughter Monica, an opera singer based in New York, performed at the ceremony, accompanied by musicians from the Royal Conservatoire of Scotland.
Prof Yunus said: "Being installed as chancellor is a very happy occasion for me. As chancellor, I will share my experiences and make them see there's nothing unusual in what I do – and that they can do that too."
Prof Yunus was made an honorary doctor of letters of the university in 2008. In 2010 the university opened the Grameen Caledonian College of Nursing in Bangladesh, to improve nursing and midwifery training.
Prof Yunus returned to the university in March this year to announce the launch of the Grameen Scotland Foundation, a charitable trust which will use the micro-lending system to support business development in Scotland.
The foundation will lend money to those who wish to start or expand small businesses. It is due to launch next year after a partnership deal is secured with Tesco Bank, which will supply £500,000 of the loan capital required.