Oxlade-Chamberlain was one of three major summer signings for Liverpool, who paid Roma just shy of £40m for Egyptian Mohamed Salah and agreed a club-record deal for RB Leipzig's Guinea midfielder Naby Keita, who will arrive next summer.
Gunners manager Arsene Wenger had consistently stated his desire to keep Oxlade-Chamberlain, who spent six years with the club after arriving from Southampton in a deal worth an initial £12m, rising to around £15m.
You still have [Philippe] Coutinho and [Adam] Lallana to come back to the players who performed so well at the weekend.
City remain very keen to sign Sanchez from before Deadline Day ends, though, and will improve on that initial offer.
"I want to publicly thank Arsene [Wenger], the coaching and club staff and my unbelievable team mates for all the incredible opportunities I have been given".
Liverpool boss Jurgen Klopp said he was "really happy" to have signed an "exciting" talent he "didn't need to think twice" about.
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"I'm not going to say too much today".
The 24-year-old finalised a move to Jurgen Klopp's side from Arsenal on Premier League deadline day for an initial fee of £35million.
"I watched the boys in the first few games of the season and they've got a lot of energy", Gibbs said in comments published on the West Brom website. The question is why didn't we bid this amount weeks ago when there was no rush and plenty of time to get the deal complete.
Oxlade-Chamberlain was deployed in the right full-back position for the match where he struggled to make an impact and he was eventually substituted after an hour. "I welcome him to the Liverpool family".
Neville worked with Oxlade-Chamberlain when he was England coach under Roy Hodgson.