Klopp, who joined the Reds in October 2015, signed a new six-year contract in July 2016 and that has now been extended further, BBC Sport reported.
Liverpool won the Champions League under the German last season and finished second in the Premier League.
The Merseyside club leads the top flight this season and has an eight-point lead in pursuit of a first league title since 1990.
"This club is in such a good place, I couldn't contemplate leaving," Klopp, 52, told Liverpool's website.
"For me personally this is a statement of intent, one which is built on my knowledge of what we as a partnership have achieved so far and what is still there for us to achieve.
"When I see the development of the club and the collaborative work that continues to take place, I feel my contribution can only grow.
"People see what happens on the pitch as a measure of our progress and although it is the best measure, it's not the only measure. I have seen the commitment from ownership through to every aspect and function of the club you can think of.
"When the call came in autumn 2015, I felt we were perfect for each other; if anything, now I feel I underestimated that.
"It is only with a total belief that the collaboration remains totally complementary on both sides that I am able to make this commitment to 2024.
"If I didn't, I would not be re-signing."
Liverpool lost only one game in the Premier League last season as it amassed 97 points but missed out on the title by a point to Manchester City.
This time around, the Reds are unbeaten in the league – having won 15 and drawn one of their 16 games – and hold an eight-point lead over second-placed Leicester City and a 14-point advantage over Manchester City.
Klopp’s men host Watford on Saturday before their main squad heads off to Qatar to play in the FIFA Club World Cup.
Liverpool has also progressed through to the knockout stages of the Champions League as it attempts to defend a trophy it won in June by beating Tottenham in Madrid.