San Jose, 18, will move for a fee of around £270,000. Bilbao were aiming to use the youngster in their second team next season, but a club statement said: "For us it is bad news, but Mikel has decided on the choice of Liverpool and it was impossible for us to fight against a European giant."
San Jose added: "It was a surprise for me but I have decided to accept the chance at Liverpool.
"I am very excited but now I know that I have to work more each day to get in the first team."