The Reds have agreed to pay the £48m release clause that will allow him to move next summer, plus an undisclosed premium.
The 22-year-old had been one of Jurgen Klopp's primary targets this summer, but Leipzig had refused to sell.
The deal will surpass the £35m paid to Newcastle for Andy Carroll in 2011.
The German side finished second behind champions Bayern Munich in the Bundesliga last season, allowing them to qualify for the Champions League group stage.
Liverpool had already had two offers for the Guinea international rejected this summer - the second understood to be around £70m - but now a compromise deal has been reached where Leipzig keep their prize asset this season and manager Klopp gets the player next summer.
So far this summer, Liverpool have signed winger Mohamed Salah from Roma for £34m, full-back Andrew Robertson from Hull for £8m and striker Dominic Solanke after his contract at Chelsea expired.
The Anfield club are also prepared to test Monaco's resolve to keep midfielder Thomas Lemar with an offer of about £60m before Thursday's transfer deadline.
Earlier this month Naby Keita was described by Schalke's sporting director Christian Heidel as being like "two players". He is right.
While Liverpool won't be able to get away with playing with 12 men, as Heidel joked at the time, he does effectively play two positions at the same time.
He is both a number eight and a number 10 in that he wins plenty of tackles and has that wonderful ability to emerge with the ball when it looks almost impossible to do, at the same time his dribbling skills are reminiscent of Sadio Mane. He will pick apart your defence with a clever through ball too.
It's pointless to talk about whether he is worth the club record fee. It is 2017 and these days buying a footballer is no different to buying a house - they are worth what someone is willing to pay.
I know that the concept of purchasing someone who you won't be able to play for a year is alien to the Premier League but it is common place in Germany.
I suspect Jurgen Klopp will have had no qualms with it and the former Borussia Dortmund manager will have been one of the key factors in Liverpool getting their man.