The specialist team will be located at the Gartnavel Hospital site, with experts seeing their first patients in January next year.
The centre will deliver residential courses for patients and carers on how to cope with the effects of chronic pain, and how to manage their condition.
Patients in Scotland have to travel to a unit in Bath, Somerset, about 400 miles from Glasgow, for such highly-specialised care.
The facility is expected to be running at full capacity by 2016. Details of the new centre of excellence were announced by Public Health Minister Michael Matheson.
He said: "Chronic pain can be distressing and difficult to deal with, but we know that if the condition is managed well, it can make a huge difference.
"That's why this new national service, based at a single location, will have a truly positive impact on people's lives.
"The establishment of this new national service in Scotland is a major milestone for people who suffer from chronic pain.
"We're determined that patients will have access to the very best services without having to take the long journey to the south of England. This new national centre comes on the back of a £1.3 million investment in chronic pain services nationally. We are working closely with NHS Greater Glasgow and Clyde to ensure that the new facilities are up and running as soon as possible."
Chronic pain is defined as pain that persists for 12 weeks or more. About 223,000 Scottish adults, or more than 5 per cent of the population, are thought to experience severe chronic pain.
Professor Blair Smith, national clinical lead for chronic pain, said: "The care and treatment that the residential service will provide represents an important part of our ambition to improve the lives of people living with chronic pain.
"This new national service also presents Scotland with an excellent opportunity to build on our experience of developing world recognised research, with the aim being to deliver continuing improvements in the treatment and management of chronic pain."