The contractor called in administrator Baker Tilly earlier this month after running into financial trouble.
Baker Tilly confirmed the firm has now been sold to new buyers but declined to reveal their identity until all creditors had been informed.
Stonewest was established in the 1950s and has worked on the restoration of a host of historic buildings including St. Paul’s Cathedral and St. Pancras International.
Joint administrator Matthew Wild said: “We are pleased to have concluded the sale thereby securing the future of this long standing business and preserving 128 jobs.
“The outcome also helps to ensure the continuance of valuable specialist trade skills.
“The company has an excellent reputation and we are delighted that the transaction provides the opportunity for it to continue to trade and build upon that reputation for years to come.”
Two other companies in the group – Rattee & Kett Limited and St Blaise Limited – had ceased trading prior to the appointment of Baker Tilly with the loss of more than 60 jobs.