The deal will take the listed firm private and marks the latest stage of a remarkable 20 years for the business.
One of the most famous names in the industry sold its construction division to O’Rourke for £1 in 2001 after a string of losses on high profile projects.
It also sold its house building activities to George Wimpey and its property development business to Kier as John Laing focused on infrastructure investing across more than 150 project during the ensuing years.
Will Samuel, Chairman of the Board of John Laing, said: “The John Laing Board believes that the offer from KKR represents an attractive and certain value in cash today for John Laing shareholders and reflects the high quality of the business, its people and future prospects, as well as providing a positive outcome for John Laing pensioners.
“KKR is a strong partner, providing long-term capital and global expertise to accelerate John Laing’s strategy, growing the development capacity and assets of John Laing and creating opportunities for our employees and broader stakeholders.
“This is particularly relevant in the current environment where there may be significant opportunities to invest in critical infrastructure which responds to public needs.
“I am proud of John Laing, an established leader in the infrastructure market with unique expertise, strong relationships and talented employees. I believe that the business and its people will continue to be well supported by KKR and we welcome the commitments provided to all our stakeholders.”