The 20-year-old has agreed personal terms and completed a medical at the club's Melwood training ground to become the Reds' second signing of the January transfer window
The Brazil international joined the Serie A side from Vasco da Gama in 2010, and spent the second half of last season on loan at Spanish side Espanyol.
The Premier League side agreed an £11.8 million transfer fee with Inter after seeing their initial bid of £6.5m rejected.
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"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 becomes the Reds' second signing of the January transfer window after the move to sign Daniel Sturridge, with only one day remaining to complete any other deals.
Southampton were also interested in the playmaker following his work with new Saints boss Mauricio Pochettino at Espanyol, but Coutinho made his preference to sign for Liverpool clear.
Liverpool managing director Ian Ayre added: "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 will wear the No.10 shirt.