The appointments coincide with the 15th anniversary of SIS, which has invested more than £53 million in 250 organisations since its formation.
Rice, the former head of Lloyds Banking Group in Scotland, was instrumental in SIS’s establishment in 2001, while Alexander was communities minister when the former Scottish Executive contributed to the start-up costs of the lender.
SIS chairman Nick Kuenssberg said: “As one of the first examples of social finance in the UK, SIS has consistently shown that social investment can increase financial sustainability, delivering longer lasting social impacts which ultimately help to improve the lives of more people.
“I’m proud that our focus on supporting the most marginalised communities has been unwavering and I’m very grateful to all of those who have supported SIS since its creation.”
Previous chairs of the SIS board Ray Perman and Alf Young and former SIS trustees Sarah Smart and Kenneth Ferguson have also been named as patrons.
Deputy First Minister John Swinney, who attended a celebratory dinner at new social enterprise restaurant Home in Edinburgh, added: “As a government, we are fully committed to supporting social enterprises to flourish, as underlined by our national social enterprise strategy, to be published later this year.”