Liverpool opened talks with Arsenal on Wednesday afternoon, quickly agreeing a deal reportedly worth £35 million, with the midfielder earning £120,000-a-week.
Oxlade-Chamberlain is currently with the England squad for the international break, but will link up with Klopp’s side ahead of their clash with Man City on September 9.
He made his breakthrough with Southampton in 2010, playing a key role in their promotion to the Championship before joining the Gunners ahead of 2011/12.
But failing to tie down a regular position under Arsene Wenger, instead employed in a utility role, Oxlade-Chamberlain pushed for a move this summer.
Turning down the Premier League champions, Oxlade-Chamberlain reiterated his desire to work under Klopp on Merseyside.
Oxlade-Chamberlain is yet to be given a squad number at Liverpool.