The UK-based Liberty House Group, led by Indian-origin executive chairman Sanjeev Gupta, said the deal secures the future of around 1,700 jobs directly, and thousands more in the supply chain and regional economy.
UK business secretary Greg Clark said: "Acquiring Tata's Speciality Steels business in South Yorkshire and West Midlands, which manufactures high quality steel for some of the UK's world leading industries such as aerospace and automotive is a great opportunity for Liberty House.
"We want to work with the steel industry on proposals to transform and upgrade their sector as part of the modern Industrial Strategy so we can build on our strengths and extend excellence into the future," he said.
The sale follows an extensive due diligence period, after the parties entered exclusive discussions last November.
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"Today's news also marks another important step forward in realising a more sustainable future for our Port Talbot based supply chain in the UK," he said.
The deal will make Liberty House one of the largest steel and engineering employers in the UK, with more than 4,000 workers at plants located across Britain's industrial heartlands.
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The business has the capability to make around 1.1 million tonnes of liquid steel per year from recycled scrap, melted in two electric arc furnaces at Rotherham.
Liberty said the Speciality Steels acquisition is a major step forward for its GreenSteel strategy, involving the recycling of UK scrap using renewable energy.
Gupta said: "I am proud that we are acquiring a world-class business with a very skilled workforce and broad range of high-value products. It is one of only a handful of such operations in the world and I am confident it will flourish within our group.
"Fulfilling the next key stage of our GreenSteel vision is incredibly exciting. We will now be able to melt scrap steel to create high-value-added products and I hope that, in due course, we will do so using renewable power."
Completion of the transaction with Tata Steel UK remains subject to necessary regulatory clearances.
Tata Steel UK is currently consulting with its employees on a number proposals that would help secure jobs across its wider business.
It is in discussions with the British Steel Pension Scheme (BSPS) trustee and the Pension Regulator to develop a "structural solution" for its UK pension scheme.
The BSPS is one of Britain's largest pension schemes, with 130,000 members, andTataSteel had inherited the scheme when it bought Corus in 2007.
The group has been in talks with German major ThyssenKrupp for a potential merger, which is also predicated on a solution to the pension scheme.
Tata Steel workers' unions began voting on a rescue plan last month and the result of the ballot is expected in coming weeks.
In March last year, Tata Steel had announced plans to sell its UK business as the company battled to control its "deteriorating financial performance".