The 20-year-old becomes Liverpool's second signing of the January transfer window following the arrival of striker Daniel Sturridge at the start of the month.
Coutinho 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."
Coutinho, who has one cap for Brazil, began his career at Vasco da Gama before moving to Inter Milan in 2010 - and the player also enjoyed a loan spell at Espanyol.
Liverpool managing director Ian Ayre said: "We're always delighted when we get the players we go after.
"It has been a successful transfer window for us, coming off the back of acquiring Daniel Sturridge from Chelsea and now Philippe from Inter Milan.
"I think that bodes well for us for the rest of the season and the future."