Liverpool will discuss personal terms with the Spaniard when he arrives on Merseyside for his medical at their Melwood training ground this afternoon.
Enrique, 25, will cost Liverpool in the region of £6million but will fill a position which they struggled with last season.
"Liverpool FC confirmed today that they had agreed a fee with Newcastle United have been in negotiation with for the transfer of Jose Enrique," said a club statement.
"The club have now been given permission to discuss personal terms with the player, who will travel to Liverpool to undergo a medical."
Enrique joined the Magpies for £6.3million from Villarreal in August 2007 but was in the final year of his contract at St James' Park and had made it clear he would not be signing a new deal.