The Indian-owned firm announced the signing of a Letter of Intent with Liberty House Group to enter into exclusive negotiations for the potential sale of the business for £100 million.
The Letter of Intent covers several South Yorkshire-based assets, including the Rotherham electric arc steelworks, the steel purifying facility in Stocksbridge and a mill in Brinsworth, as well as service centres in Bolton and Wednesbury.
Speciality Steels employs about 1,700 workers, who produce steel for the aerospace, automotive and oil and gas industries.
Bimlendra Jha, chief executive of Tata Steel UK, said: "The Speciality Steels business is independent of the pan-European strip products supply chain and today's announcement is in line with the overall restructuring strategy of the UK portfolio.
"This is an important step forward in seeking a future for Speciality Steels and we have reached this stage thanks to the efforts of employees, trade unions and management.
"We now look forward to working with Liberty on the due diligence and other work streams so that the sale can be successfully concluded. We will continue to work closely with trade unions and will communicate any material news on this issue to the employees on an ongoing basis."
Roy Rickhuss, general secretary of the Community union, said: "After months of uncertainty and delay from Tata, this will be welcome news for the thousands of steelworkers whose jobs depend on the success of this business.
"Community has spent months campaigning to save these jobs and today's news is a credit to our local reps who have worked so hard to ensure the business has a viable future. We will now begin the process of working closely with Liberty to examine their plans to make a success of Speciality Steels.
"The number one priority for Community will be ensuring that Liberty have a proper plan to protect jobs and provide the long term investment necessary to grow the business. Crucial to this plan will be ensuring that the business' loyal workforce have a pension plan that provides dignity and security in retirement."
Sanjeev Gupta, executive chairman of the Liberty House Group, said: "We look forward to working with Tata Steel over the coming weeks to complete this hugely important milestone transaction.
"We recognise the world-class skills of the Speciality Steels workforce and are eager to join with them to develop the business and increase market share, both domestically and internationally using our global presence. As part of that process we will now engage fully with the trade unions and the local community. We are counting on their full support."
Liberty House and Tata Steel expect the acquisition to complete early in the first quarter of 2017.
Unite national officer Harish Patel said: "Today's announcement is welcome as we can at last see some movement towards certainty for our members.
"Our key concerns are job security for the workforce, the future of the British Steel pension scheme and what the investment plans will be from the Liberty House Group going forward.
"Of course, the devil is very much in the detail, which is why we will be asking Tata Steel to ensure that we can conduct independent due diligence on its proposals.
"As a matter of urgency, we must see security for the pension scheme to which men and women have dutifully contributed all their working lives.
"Our hard-working members, their families and their local communities have lived with a dark cloud of uncertainty hanging over them for more than a year."