A total of 26 people with disabilities, who were made redundant as a result of the closures, have been recruited to work at the Haven PTS Ltd factory in Stirling.
Health Secretary Alex Neil joined enterprise minister Fergus Ewing to launch the textile manufacturing business, which has been awarded a three-year contract for nurses' uniforms for the NHS in Scotland, worth up to £1.5 million a year.
Mr Ewing said that by last month, fewer than half of the 250 people who lost their jobs as a result of the Remploy closure had started in a new position.
The Scottish Government has since launched a new directory to showcase the work of supported businesses - firms where more than half of the workers are disabled and would be unable to work in the open labour market.
Mr Neil said: "I am delighted nurses' uniforms for the NHS across Scotland will be provided by Haven PTS Ltd and that this work has enabled the company to take on former Remploy employees.
"This work will enable Haven to provide up to 150,000 tunics and 100,000 pairs of trousers each year, providing sustainable jobs and helping to stimulate the local economy."
Mr Ewing said: "I chaired the Remploy stakeholders group, which sought to explore any possible future employment opportunities for affected Remploy employees, and I am delighted our hard work has resulted in Haven PTS Ltd being able to take on 26 members of staff.
"Without these new opportunities, all of the Remploy staff would have been left unemployed and struggled to find new jobs."