The Italy national team player has given the green light for the transfer, with Liverpool agreeing to pay a reduced fee of €13m to secure the signing of the European Championship winner.
Chiesa has been frozen out at Juve and encouraged to find himself a new club before Friday's transfer.
Transfer expert Fabrizio Romano is reporting: "BREAKING: Federico Chiesa to Liverpool, here we go! Agreement done for €13m initial fee with add-ons.
"Four year contract for Chiesa as new Liverpool player, set to fly later today.
"Chiesa accepted Liverpool immediately. Deal DONE. Exclusive story confirmed."