Arsenal manager Arsene Wenger spoke last week of his desire to keep the 24-year-old Oxlade-Chamberlain, who was also a target for champions Chelsea.
But the player had his heart set on a move to Liverpool, who beat Arsenal 4-0 in the league on Sunday, and rebuffed Chelsea’s advances.
He will become Liverpool’s second most expensive signing after Guinea international Naby Keita, who will join the club from next season for 48 million pounds from Germany’s RB Leipzig.
Oxlade-Chamberlain made more than 130 Premier League appearances for Arsenal since 2011. He can play in central midfield or on either flank and his versatility is one of the reasons Liverpool manager Juergen Klopp was keen to bring him to Anfield.