The 24-year-old Greek international has joined from Olympiacos in a £11.75m deal and has signed a five-year contract.
Tsimikas, who featured against Wolves in the Europa League last week, will provide much-needed competition for Andy Robertson on Merseyside.
Klopp believes his newest recruit will fit right in with the Premier League champions.
“We have watched Kostas for a long time and are really happy that he has joined us. It’s the perfect news before we come back together very soon,” he told the club’s official website.
“He is a very good footballer with an attitude to win and to compete, and I really like his mentality. It fits perfectly with the mood and the desire we have in our dressing room already.
“He has showed already at a young age he can experience football in a different country and do well – and he has been a big part of the success Olympiacos has had to win their title this season and in their European campaigns.
“Kostas knows from personal experience what is required to challenge and succeed domestically and in the Champions League, and he is ambitious for more – just like us.
“He has come up against some very tough opponents in the past couple of seasons and done well and we know he relishes the challenge, which is perfect for us.
“For that reason we are delighted to know we’ll have him with us for the years ahead. I’m so pleased.”