The 20-year-old becomes Liverpool's second signing of the January window after Daniel Sturridge joined from Chelsea earlier this month.
The transfer fee was undisclosed, but was reported by British media to be around 8.5 million pounds.
"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," the player said on the club website.
"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 has won one cap for Brazil and moved to Inter from Vasco da Gama in 2010.
After showing early promise, he failed to nail down a starting spot at the Serie A club and was frequently criticised for being too lightweight for the demands of the Italian top flight.
He was loaned out to Spanish side Espanyol last season and enjoyed a purple patch in which he scored five goals in 16 appearances.
Liverpool managing director Ian Ayre said the club had to fight hard for the Brazilian's signature amid rumours of interest from Southampton.
"We're always delighted when we get the players we go after," Ayre said.
"We certainly fought off strong competition from others. In the early parts of discussions, I know Inter Milan were reluctant.
"But we did some good work, the whole team that work around this got involved and I'm pleased to say we secured him."
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