The 20-year-old is believed to have been in talks with the Reds for the last few days and and was spotted at the club's Melwood training ground yesterday afternoon.
Those talks have been successful and Coutinho, who will wear the number 10 shirt, has signed a "long-term contract" at Anfield.
"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," he told the club's official 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."