The Brazilian playmaker passed a medical on Monday during which Barcelona doctors analysed the injury that kept him out of Liverpool's Premier League win over Burnley on Jan. 1.
"Coutinho has an injury in his right thigh. He will be out for 20 days," Barcelona said in a statement, meaning he is likely to make his debut in the Catalan derby against Espanyol on Feb. 4.
Barcelona agreed a 142 million-pound deal with Liverpool on Saturday to buy Coutinho, who became their record signing.
The Brazilian was presented to more than 7,000 fans at the Nou Camp and later told reporters that it was a dream for him to play for his new club.
"I am really happy, it's a dream and of course I am here thanks to many people," said Coutinho.
"Firstly God, my family, my parents, my partner, my daughter, they are with me through every moment. The effort of Barcelona, the president, the directors.
"I am also grateful to Liverpool for the five years I spent there. The directors understood it was my dream, they would have liked me to stay but it was my dream to come here and they understood.
"They were men of their word, and the (Liverpool) fans, we had good moments together. I am happy to arrive here at my new home."
Coutinho's debut will have to wait because of his injury, but the player is anxious to make an impact at his new home.
"Many, many times, I have dreamed of scoring my first goal, important goals," added Coutinho.
"I've dreamed of playing here many times. My job is to work hard to be available."
(Reporting by Rik Sharma, editing by Ed Osmond and John Stonestreet and Christian Radnedge)
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