Coutinho, 20, completed his £8.5million move to become Brendan Rodgers second signing during the Janaury transfer window following Daniel Sturridge's move from Chelsea.
The Brazilian youngster has been in Liverpool for the last few days while he underwent a medical and other formalities including a work permit.
Coutinho was delighted to sign for Liverpool and said: "I'm feeling very happy, it's a very important step in my career and I'm expecting to come here and play good football to give my contribution on the pitch.
"Liverpool is a great club with great players. We've always heard about Liverpool's history in Brazil. They are the club that have been interested in me and that have showed this interest so I know they believe in me and my football."
The young Brazilian began his career with Vasco de Gama before moving to Italy with Inter Milan in 2010. The midfielder was sent on loan to Espanyol last season after struggling to find first-team football with Inter.
Coutinho is the fifth Brazilian to represent the club after Fabio Aurelio, Diego Cavalieri, Doni and Lucas Leiva. The Brazil international can either play behind the striker, as a winger and as a left striker.