Elliott Advisors did not disclose how much it was paying for the majority interest in the chain, which has 283 stores in the UK and Ireland employing more than 3,000 staff.
Sky News first reported Elliott’s interest back in January.
Current owner Lynwood Investments would retain a minority stake under the deal, Waterstones said, while its chief executive of seven years, James Daunt, is being retained by the new owner.
The chain’s fortunes have recovered over its past two financial years to record profitability.
It has benefited from a faltering challenge from eBooks, with profits growing to £18m in the 12 months to April 2017 on sales of £400m.
Nevertheless, times have been tough on the high street over the past 12 months – with consumers feeling the pinch from an economy that has seen wages rise at a slower pace than prices until recently.
Paul Best, head of European private equity at Elliott, said: “As the leading physical book retailer in the UK, Waterstones is a mainstay of UK high streets and has a huge and loyal customer base.
“We look forward to supporting James Daunt and his entire team over the long-term as they continue to build and grow the business.”
Mr Daunt added: “This is a very happy outcome for Waterstones.
“Our booksellers can be immensely proud to have proved through good, old-fashioned bookselling, the enduring appeal and worth of real bookshops.”
Elliott has a reputation as a so-called “activist investor” in companies it does not control.
The hedge fund, which has £35bn under management, was successful earlier this week in its demand that Whitbread spin off Costa Coffee to secure greater value for investors.
It had recently become the biggest shareholder in Whitbread, which also has the Premier Inn hotel chain in its stable.