Speaking to the club's official website, the Brazilian highlighted the difference the former Borussia Dortmund coach has made since arriving at the club.
"It's great news for the club and for the fans as well because the relationship with him started really well and we hope that he will have a lot of success at the club," he said.
"He came eight, nine months ago. We got to two finals last year and of course this is the first full season we will have under him."
Leiva, who has been subject of speculation regarding his future at the Reds, said that Klopp wants to implement change within the team, without affecting them too much.
"About the new contract - it's always good, because it shows that the club believe in what he is doing and the decisions he is making.
"He's trying to change [things] step by step without affecting the team so much," the 29-year-old concluded.