Barcelona did not reveal the cost of the deal for the 25-year-old playmaker but a person familiar with the details told The Associated Press that the transfer could be worth 160 million euros ($A268 million).
"The player now has permission to complete the usual formalities to conclude the transfer immediately".
Klopp said the club had "hoped" they would be able to persuade the player to stay, adding: "The club did everything within our means to convince Philippe that remaining part of Liverpool was as attractive as moving to Spain".
Klopp said Coutinho "wanted this move to happen since July", when Barcelona first made its interest known. "It is his dream and I am now convinced there is nothing left at our disposal to change his mind". You can not transfer the heart and soul of Liverpool Football Club, although I am sure there are many clubs who would like to buy it.
The Spanish league leaders had three offers for Coutinho rejected in the summer.
Coutinho's departure would be a blow to Liverpool, but it would allow Barcelona to move on from the bitter experience of losing his Brazil teammate Neymar last summer to Qatar-backed Paris Saint-Germain for a world record 222 million euros.
Meanwhile, Inter Milan will miss out on a huge financial windfall as they did not insert a sell-on clause when they sold Coutinho to Liverpool in January 2013, a source told ESPN FC in August.
He will not be eligible to play for Barcelona in their Champions League last-16 tie against Chelsea, having already played a key role in Liverpool's qualification for the knockout phase.