The £1 deal means 4,400 UK jobs will be preserved including a steelworks in Scunthorpe, two mills in Teesside, an engineering workshop in Workington and a design consultancy in York.
The business will now trade under the name of British Steel.
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 Capital ownership, the business will continue the momentum of the improvement program that has been initiated in the last 12 months.
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"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."
Union Unite also welcomed the news, saying the deal is a "testament to the skills and sacrifice of the workforce".
The organisation's convenor for British Steel 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."
(LM)
