The businessman, who is chair of Weir Group and the Organising Committee for the Glasgow 2014 Commonwealth Games, is the university's fourth Chancellor and takes over from Lord Hope of Craighead. The university's principal Professor Sir Jim McDonald said Lord Smith would bring a "lifetime's experience in business and industry" to the role.
Lord Smith, meanwhile, praised Strathclyde's vision to be a leading international technological university, saying Scotland needed "a university which is at home in partnerships with business and industry".
"Universities are places of drive and energy, places where the impossible is just another challenge which can be overcome, they are communities of the young and the wise, working in common cause to make things better. Universities are exceptional places, and Strathclyde is among the most exceptional."
Lord Smith was installed as Chancellor at a ceremony in the Barony Hall, Glasgow.
Sir Jim McDonald said: "Strathclyde is a place that likes to get things done, and business appreciates and recognises that.
"Our purpose is to make a contribution to economic, social and cultural development by working with the leaders of today through direct engagement, and inspiring the leaders of tomorrow in lecture theatres and the laboratory. We look to Lord Smith to support us."