Union bosses welcomed the return of British Steel as Tata Steel confirmed it sold its Long Products Europe business to Greybull Capital.
The Community union's general secretary, Roy Rickhuss, said: "Community warmly welcomes the opening of this new chapter in the course of the UK steel industry.
"It also demonstrates that there is the chance of a brighter future for steelmaking in the UK, with the right vision and investment."
Businesses affected in the UK include the Scunthorpe steelworks, two mills in Teesside, an engineering workshop in Workington, a design consultancy in York, and associated distribution facilities.
There is also a rail mill in France.
All of the businesses will be trading under the name British Steel.
Mr Bimlendra Jha, Executive Chairman of the Long Products Europe business and CEO of Tata Steel UK said: “As a responsible seller, Tata Steel is delighted to have secured a buyer for this business and we hope that under Greybull ownership, the business will continue the momentum of the improvement program that has been initiated in the last 12 months.
"Employees and trade unions have worked closely with the Long Products Europe management team to improve the business’s prospects, putting it in a more competitive position than it has been for many years."
The sale has saved 4,800 jobs - most of them based in the UK and 400 in France.
Tata Steel has yet to find a buyer for the bulk of the UK business, but according to the Financial Times, will announce the preferred bidder on June 24.