The US-based FSG said they had agreed the deal with 1892 Holdings, a consortium led by British-Indian millionaire Amit Bhatia, also featuring Bezos and Eduardo Saverin, who co-founded Facebook.
Reports suggest the group have acquired a stake of about one-third of the club, valuing Liverpool somewhere between £5 billion and £6 billion.
Bezos, the fourth-richest person in the world with an estimated net worth of £189bn, is not expected to join the club's expanded board of directors.
Bhatia is set to become the Reds' vice-chairman, while Bryan Baum, founder of venture capital firm K5 Sports, which Bezos is using to invest in Liverpool, is expected to join the Anfield board alongside Saverin’s wife, Elaine.
“Liverpool has always been built by thinking beyond one season and making decisions with the club’s long-term interests in mind. That approach continues to attract interest from respected investors and business leaders around the world,” FSG president Mike Gordon said in a statement.
“As we considered this opportunity, it became clear that Amit and the consortium shared our long-term philosophy and appreciation for what makes Liverpool special.”
With several weeks until the Premier League transfer window closes, the new investment could be a boost to Reds boss Andoni Iraola as he looks to strengthen his squad for the new season.
Bhatia has extensive experience in football boardrooms, having spent 18 years as a co-owner of QPR before stepping away from the Championship club after his proposed Liverpool investment became public.
“We are incredibly proud to be investing in Liverpool Football Club and to be doing so alongside FSG. We have the utmost respect and admiration for FSG as owners and for everything they have achieved at Anfield,” Bhatia said.
“To be welcomed as a partner in a club of this stature is a huge privilege. We are making this investment because we believe deeply in Liverpool and its leadership, and we look forward to supporting the club’s continued success for years to come.”
Liverpool are next in action against Como at Anfield on 16 August.