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 - at Anfield.
Sean O'Driscoll, who was Rodgers' assistant, has left the club, while Gary McAllister has been moved from first-team coach to a new "ambassadorial position".
Klopp will be officially introduced by Liverpool at a news conference at 10:00 BST on Friday.
After seven years as Mainz boss, Klopp joined Dortmund in 2008 and led them to two Bundesliga titles.
They lost to Wolfsburg in last season's German Cup final - his final game - at the end of a campaign in which they struggled domestically, finishing seventh in the league.
Klopp takes over a Liverpool side who have won only four of their 11 games in all competitions this season.
The international break means his first game in charge is a trip to Tottenham in the Premier League on 17 October.
Klopp will have to work within the existing structure and what has become known as Anfield's 'transfer committee'
It is the group that plans and carries out transfer strategy and up until Sunday night consisted of Rodgers, scouts Dave Fallows and Barry Hunter, the man in charge of analysis Michael Edwards, FSG's Anfield representative Mike Gordon and chief executive Ian Ayre.
Rodgers, who took over in June 2012, led the Reds to second place in the Premier League in 2013-14.