NESV owns a portfolio of companies including the Red Sox, New England Sports Network, Fenway Sports Group and Rousch Fenway Racing.
Liverpool chairman Martin Broughton told the club's official website: "I am delighted that we have been able to successfully conclude the sale process which has been thorough and extensive.
"The board decided to accept NESV's proposal on the basis that it best met the criteria we set out originally for a suitable new owner. NESV's philosophy is all about winning and they have fully demonstrated that at Red Sox.
"We've met them in Boston, London and Liverpool over several weeks and I am immensely impressed with what they have achieved and with their vision for Liverpool Football Club.
"By removing the burden of acquisition debt, this offer allows us to focus on investment in the team."
The takeover is subject to the resolution of a legal dispute with US owners Tom Hicks and George Gillett. The Premier League will also have to approve the buyout.
Yesterday Hicks and Gillett tried to sack managing director Christian Purslow and commercial director Ian Ayre in a last-ditch bid to keep control of the club.
