The Premier League club's US owners, Fenway Sports Group, broke the news on Friday with one source saying the consortium's stake is about 30 per cent.
British media reports said the deal was worth more than Stg 1.5 billion ($A2.9 billion), which values the club at over Stg 5 billion ($A9.6 billion).
FSG, which bought Liverpool in 2010 for Stg 300 million ($A574 million), will maintain the majority share and operational control of the club.
The consortium, named 1892 Holdings, is led by former Queens Park Rangers chairman Amit Bhatia and also includes the Mittal Family Trusts, EE Capital and the K5 Sports fund, where Bezos is the lead investor.
"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," FSG president Mike Gordon said in a statement.
"Their experience and perspective will complement the strong foundation already in place, and we look forward to working together."
Bhatia will become the club's new vice chairman and join the expanded board along with Elaine Saverin from EE Capital and Bryan Baum from K5 Sports. Bezos will not have a seat on the board, according to the source.
Liverpool, who have been English champions a joint-record 20 times, finished fifth in the Premier League last season. They will start the new campaign at Newcastle on August 23.
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