I Will Always Cherish Liverpool In My Heart
The Brazilian forward, 25, completed his £142m move to the La Liga club on Monday after five years on Merseyside.
Coutinho said he could “never thank Liverpool fans enough” for their support and “will always cherish Liverpool in his heart”.
He added that he leaves the Reds as playing for Barcelona “is a dream”.
Coutinho scored 54 goals in 201 games at Liverpool and he said he hope he had “delivered memories and moments that have brought happiness to the Liverpool supporters”.
His Instagram post came on the day he was unveiled at Barcelona following a protracted move.
Liverpool rejected three Barcelona bids and a transfer request from the player during the summer transfer window.
Coutinho is now reported to have committed £11.5m of his own money to help facilitate the deal.
“I hope the supporters understand that choosing to experience something new is not about diminishing their importance to me or the club’s importance,” Coutinho added.
“Nothing will ever diminish that in my heart.”