The Scottish Islet Isolation Laboratory is the only one in the UK to operate 24 hours a day.
The islet transplant programme extracts islets (cells which produce insulin) from a donated pancreas and injects them into the liver of someone with Type 1 diabetes and those who have had a kidney transplant.
In its first year the centre aims to treat 12 patients but this figure will depend on the number of organs provided for transplant.
The programme is awaiting its first donated pancreas before treatment can begin.
Kimberley Hall, whose two daughters Amy, 11, and Kirsty, 7, have Type 1 diabetes, was at the laboratory opening in Edinburgh.
The 30-year-old from Peebles also has Type 1 diabetes. She said: "It will change my life and the girls as well. I will be able to take them to parks on my own.
"There is a light at the end of the tunnel for the girls as well. It's pretty amazing.
"At this moment in time it's not confirmed that I will be accepted for it but hopefully it does go ahead."
Mrs Hall had a pancreas transplant in 2006 but her body began rejecting the organ in November last year.
She now has to inject insulin four times a day and must have an adult with her in case she collapses.
Speaking about having the transplant, she said: "It was so fantastic and amazing.
"It's been really difficult and hard having no quality of life and having someone with me all the time."
Speaking at the opening of the laboratory, Public Health Minister Shona Robison said: "The programme's creation represents a significant investment by NHS Scotland in helping to tackle a condition that affects increasing numbers of young people.
"It's also made possible by the close collaboration between the pancreas transplant programme at the Royal Infirmary of Edinburgh, the Scottish National Blood Transfusion Service and the Scottish Centre for Regenerative Medicine.
"The Scottish Government is investing in a range of initiatives designed to increase the number of actual organ and tissue donors in Scotland, so that programmes like this can continue to save and improve lives."
John Casey, lead clinician for the islet cell programme, said: "Islet isolation is a new and highly skilled technique which can prove lifesaving for some patients who are unaware of the level of sugar in their blood.
"This technique depends on organ donors but work at the Scottish Centre for Regenerative Medicine at Edinburgh University gives hope that in the not-too-distant future islets will be able to be produced from stem cells."
The programme is a joint project by Lothian Health Board, the Scottish National Blood Transfusion Service (SNBTS) and Edinburgh University.
Keith Thompson, an SNBTS director, said: "For nearly 80 years the Scottish National Blood Transfusion Service has been taking red blood cells from one person and processing and testing them so that they can be safely given to patients in need.
"Being able to do this now with islet cells is a major step forward and our new state of the art laboratory has been specifically designed, equipped and staffed to achieve this.
"We hope that islet cells prepared here will be able to transform the lives of diabetics who would benefit from this advanced treatment."
"The development of novel cell therapy in Scotland will be significantly enhanced by the experience that we gain in this islet cell programme.
Type 1 diabetes is a condition frequently diagnosed in childhood or adolescence. Patients depend on insulin to survive.
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