"It's one of the best moments in my life, to be here with my family. We are here together and it feels like a dream," the ex-Borussia Dortmund manager told LFCTV.
Explaining what attracted him to the city and the club, Klopp said: "Perhaps Liverpool is the most interesting job in world football at the moment.
"I always thought about working in England because of the kind of football and the intensity of the football, and Liverpool was first choice. Now I have got the opportunity to work here, it's the best thing I can imagine.
"It was a crazy day, with all that happened in Germany and all that happened here. It's absolutely a great feeling for me, it's a big honour for me.”
Looking to the future of the club, Klopp remained realistic.
"I'm not the guy to say ‘this year will be the best year in the history of LFC'. If it happens, we can celebrate. If not, we have to work further," he said.
Liverpool's director Ian Ayre told reporters that Klopp "told us he wouldn't have broken his sabbatical for any other job".
A press conference will be held at 11am (12pm GMT) at Anfield, at which Klopp will first meet the British media.