The Brazilian midfielder, who arrives for a fee of around £8.8m, said that he hopes to repay the supporters on the pitch.
"I'd like to thank all fans that have sent me messages on Twitter," Football Italia quotes Coutinho as saying.
"I'm coming here very keen to help the club with my moves and scoring goals to put Liverpool at the top. I just want to say thanks.
"I'm happy to be signing with a great club and I hope I can give them my contribution."
Coutinho has one cap for his country.