The Brazilian youngster is arriving from Vasco da Gama, having signed for Inter almost two years ago.
"I am very happy to be here. I hope to win many titles and give the Inter fans many satisfactions," Coutinho said.
"The first few days have gone calmly. There are two Brazilian team-mates here and I find myself well.
"I am studying your language, but I already understand it slightly even if I speak slowly."
He added: "Robinho and Kaka inspire me. I really like watching them a lot on TV.
"When I knew of Inter's interest I was flattered. It's the dream of every Brazilian player to play for a big club in Europe and Inter are a big club."
Inter boss Rafael Benitez appeared to be happy with Coutinho's arrival.
"Coutinho is a quality young player who can be the future of the club. The fans have been surprised by his quality in training and he can do very well," Benitez concluded.