Unions have welcomed the return of the British Steel brand after the completion of the sale of part of Tata Steel.
Greybull Capital has bought the Long Products business, securing thousands of jobs at a huge plant in Scunthorpe, as well as those at a design consultancy in York.
Tata continues to assess bids for the rest of its UK business - which include sites in Rotherham, Stocksbridge and Port Talbot, Wales.
Greybull is renaming the Scunthope business British Steel - a name which disappeared in the 1990s.
Bimlendra Jha, chief executive 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 Capital ownership, the business will continue the momentum of the improvement programme 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. It is through their dedication and hard work that we are in this position today in spite of continued challenges in the market."
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.
"British Steel is built on firm foundations with a skilled, experienced and dedicated workforce determined to make a success of the business.
"They have a proud track record of delivering high-quality long products to flagship construction and infrastructure products around the world. The turnaround plan agreed between management and unions is already yielding positive results."
The Long Products business includes the Scunthorpe steelworks, two mills in Teesside, an engineering workshop in Workington, a design consultancy in York, and associated distribution facilities, as well as a rail mill in northern France.
The business employs 4,800 people - 4,400 in the UK and 400 in France.
British Steel commercial director Peter Hogg said it was a landmark day for the business.
He said: "Today marks the first day of business for our new company and we are delighted to be launching under the iconic British Steel brand.
"It has taken a huge amount of effort and a strong partnership between our employees and their union representatives, our customers and our suppliers, and many months of hard work to get to this point. We also appreciate the help and support from both local and national government and our local MPs.
"Our industry has faced challenging times over the last few years, but we are confident that our new venture, built on our core values of pride, passion and performance, will not only reinvigorate this business, but position it as a world leader.
"Our heritage is important to us. For decades our skilled workforce has dedicated itself to producing the highest quality steel that has been used in landmark buildings and infrastructures projects around the world. The launch of British Steel will enable us to build a stronger future for both our employees and all those who do business with us."
Unite's convenor in Scunthorpe, Martin Foster, said: "British Steel's first day of trading marks the beginning of a new chapter not only for Scunthorpe, but UK steelmaking. It is a massive vote of confidence in a world class workforce and the town of Scunthorpe with its proud history of steelmaking.
"Bringing months of uncertainty to an end, it shows that steelmaking in the UK can have a future. Over the coming months we will be working with the new owners to make the new British Steel a success and ensure it goes from strength to strength.
"It should not be forgotten, though, that today would not have been possible if it had not been for the sacrifices the workforce has made as part of the firm's transformation plan. For many it has involved tough choices about pay and their jobs.
"They will be working hard to make sure British Steel has a bright future with the expectation that they will share in its future success."
Unite general secretary Len McCluskey said: "Today's first day of trading for British Steel is testament to the skills of the workforce and their union representatives who have worked hard to secure the future of Tata Steel's former long products division."
Business Secretary Sajid Javid said: "Today's deal is fantastic news for the steelworkers of Scunthorpe, Teesside, Workington and York. This investment is testament to the immense skill of the local workforce, the potential of these plants and a vote of confidence in the UK steel industry as a whole.
"The name British Steel has a long and proud history and today's news underlines the Government's belief that there really is a viable, sustainable future for world-class steelmaking in this country."