After the 20-year-old Brazilian successfully completed his medical and acquired his work permit, the Premier League club announced they have signed a long-term deal with the attacking midfielder. Coutinho becomes manager Brendan Rodgers' second signing of the January transfer window having already brought in Daniel Sturridge from Chelsea for £12m.
"I'm feeling very happy," said Coutinho. "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 began his career in Brazil with Vasco da Gama before moving to Inter Milan in 2010. He has also spent time on loan in Spain at Espanyol.
Liverpool managing director Ian Ayre told the club's official website: "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."
Coutinho only has one senior Brazil cap but he represented his country at the FIFA U-17 World Cup Nigeria 2009 and the FIFA U-20 World Cup Colombia 2011.