Coutinho, 20, can play as a central playmaker or a wide midfielder and takes the club's No. 10 shirt after signing what Liverpool describe as a "long-term contract."
The Brazilian, who has won one cap for his country, is the club's second January signing after the £12m capture of Daniel Sturridge from Chelsea.
"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," Coutinho said.
"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 started his career with Vasco da Gama before joining Inter for 4 millon euros in 2008.
He had to wait until his 18th birthday to join the club formally but then impressed in the first half of the 2010-11 season under former Liverpool boss Rafa Benitez.
Last season he joined Espanyol on loan and scored five goals in 16 appearances in La Liga.
Liverpool chief executive 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."