According to reports, the shares leapt 770p to 6570p on the news on Tuesday, valuing the business at £4.8 billion and the founders 53% stake at £2.5 billion.
The pair founded the firm in 1973 in Gloucester’s Wotton-under-Edge, and had met at Rolls Royce.
In a statement, the company said: "Together, the founders (and certain persons connected with them) own approximately 53% of the issued share capital of the company and have expressed a preference for the disposal of their entire combined shareholding.
"The board has considered various options with its advisers. In considering these options the board, including the founders, has had regard to the interests of all the company's stakeholders. The board has unanimously concluded that it would be appropriate to investigate the sale of the company and is therefore launching a formal sale process for the company.
"The board intends to seek a buyer who will respect the unique heritage and culture of the business, its commitment to the local communities in which its operations are based, and who will enable the company to continue to prosper in the long-term.
"Since its foundation in 1973, the company has grown into one of the world's leading engineering and scientific technology companies, with expertise in precision measurement and healthcare.
"At the heart of everything the company does lies a culture of innovation and a fundamental belief that success comes from patented and innovative products and processes, high quality manufacturing, and the ability to provide local customer support in all its markets around the globe. This has resulted in a long-term track record of strong operational and financial performance, bringing significant economic and social benefits to its local communities."
UBS is acting as sole financial adviser and corporate broker to the company in relation to the sale process.
Sir David McMurtry, executive chairman of Renishaw, and John Deer, non-executive deputy chairman, said: "We are both grateful for our continued good health, however we recognise that neither of us is getting any younger.
"Now finding ourselves in our 80s, our thoughts have increasingly turned to considering the future of our shareholdings in the Company and how we can actively contribute to securing the future success of the business. With that in mind, we approached the rest of the Board to indicate that we felt the time was now right to discuss the best way to achieve this.
"As the founders of Renishaw, we understand the importance of Renishaw’s culture, our place in the communities in which we operate, our commitment to research and development, and the loyalty of our staff, our suppliers, and the customers we serve; these together have been the foundation of our success for almost 50 years.
"With the Board, we are therefore focused on ensuring that we find the right new owner for our business – one who respects and will continue to nurture these important attributes.”
