The 24-year-old has completed a £35 million move to Anfield and Klopp believes he has the potential to become a top-class player.
"He is someone with really good abilities who always gives everything for his team," Klopp said. "A player that is positive and willing to take risks to try and make positive things happen.
"He may still be young but he has a lot of experience in the Premier League, Champions League and for his country. Already he is a very, very good player.
"I think he has the mentality and desire to get even better - and that excites me.
"This is someone making a tough decision to leave one great club and come to another great club and I think he had many options, so to get him means I am delighted."
Oxlade-Chamberlain joins Liverpool with the understanding he will be played more centrally but whether Klopp actually fulfils that promise remains to be seen.
It's become patently clear that the Englishman doesn't want to play at wing-back, as evidenced by his recent performance against his new club.
Liverpool beat Arsenal 4-0 at Anfield last Sunday, during which Oxlade-Chamberlain was terrible and constantly caught out of position.
The Ox was so bad at Anfield, in fact, that Gary Neville has trolled him on Twitter following his move to Liverpool.
In response to Oxlade-Chamberlain being pictured in Liverpool's training kit, Neville wrote: "He was one of Liverpool's best players last Sunday 😉."
Neville was only joking, of course, but Liverpool fans won't be so forgiving if Oxlade-Chamberlain produces similar displays for them this season.
Klopp has no such fears that will be the case, though, saying that the Ox has always had all the ingredients to become a top player.
"I am really, really happy we have got Alex signed," he added. "Since the last game I have been waiting and hoping we could make this transfer - and when I got the news it was fantastic.
"I remember the first time I saw him play live - it was at [Borussia] Dortmund in 2014 and he came on as a sub that day and made a big impact.
"He stood out immediately because of his pace and skills and his attitude in such a big game for a young player.
"I remember him chasing back to make a brilliant challenge on [Henrikh] Mkhitaryan in the box to save a certain goal."