Financial details were not disclosed but British media reported the minority stake was sold for between $100 million to $200m.
FSG said the investment would mainly be used to pay down debt from the COVID-19 pandemic, stadium expenses to enhance Anfield's capacity, expenses in building their new training centre, repurchasing their old Melwood training ground and summer transfers.
"Our long-term commitment to Liverpool remains as strong as ever," FSG president Mike Gordon said in a statement.
"We have always said that if there is an investment partner that is right for Liverpool then we would pursue the opportunity to help ensure the club's long-term financial resiliency and future growth.
"We look forward to building upon the longstanding relationship with Dynasty to further strengthen the club's financial position and sustain our ambitions for continued success on and off the pitch."