The 20-year-old was granted a work permit by the Home Office after a hearing in London on Tuesday.
"I'm feeling very happy, it's a very important step in my career," Coutinho told Liverpool's official website.
"Liverpool is a great club with great players. We've always heard about Liverpool's history in Brazil. I know they believe in me and my football."
Southampton were also interested in Coutinho, who becomes Liverpool's second signing of the transfer window following the capture of striker Daniel Sturridge from Chelsea at the beginning of the month.
Playmaker Coutinho, who has one cap for Brazil, is a product of Vasco da Gama's youth system.
He was bought by Inter in 2008, at the age of 16, for €4m, although the Serie A side immediately loaned him back to Vasco, because foreigners are prohibited from playing professional football in Italy until they are 18.
However, he struggled to make an impact when he returned to Italy and spent half a season on loan at Spanish side Espanyol in January 2012 before attracting strong interest from Liverpool.
"We're always delighted when we get the players we go after," said Liverpool managing director Ian Ayre.
"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."

The Assembly Speaker says support for the Commonwealth is not part of his personal politics.
However, he said he wanted his approach during his time as Speaker to be about "respect".
He did not comment on whether Ireland should become part of the Commonwealth.
"In upholding the independence and impartiality of the Speaker, my approach during my time in office is going to be one of respect," he added.
"Involvement in the Commonwealth Parliamentary Association has naturally not been part of my political life in the past.
"However, I will represent all sides of the House as any Speaker should and I intend to respect and acknowledge the culture and traditions of all sides of the assembly chamber.
"Taking up this position is a first step in demonstrating that approach.  I look forward to hosting next week's event to mark Commonwealth Day and its theme of encouraging youth participation in our democratic system."
Liverpool have completed the £8.5m signing of Brazilian midfielder Philippe Coutinho from Inter Milan.
[NEXT_CONCEPT]
Sinn Féin's Mitchel McLaughlin has announced he will take up the position of President of the NI Assembly Branch of the Commonwealth Parliamentary Association (CPA).