The 48-year-old German replaces Brendan Rodgers, who was sacked on Sunday after three and a half years in charge with the club 10th in the Premier League.
Klopp has been out of work since May, when he ended a seven-year spell at Borussia Dortmund to take a sabbatical.
He is expected to have Zeljko Buvac and Peter Krawietz - his former assistants at the Bundesliga club - as part of his coaching staff at Anfield.
Sean O'Driscoll, who was Rodgers's assistant, has left the club while Gary McAllister has been removed as first-team coach, although he is considering the offer of another role with the Reds.
No contract has yet been signed but that is viewed as a formality when Klopp arrives in Liverpool later on Thursday. He will be officially unveiled by Liverpool on Friday morning at 10:00 BST.