The Premier League champions have reached an agreement for the 29-year-old midfielder worth at least £20 million - plus £5m in add-ons - on a four-year contract.
Thiago - who is set to wear the number six shirt for the Reds - joined Bayern from Barcelona in 2013, and played in last season's Champions League final win over Paris St-Germain.
Once completed, he will become the club's second summer signing after the arrival of Greece defender Kostas Tsimikas.
According to BBC Sport, the £20m figure will be paid in instalments, and the extra £5m will depend on Premier League and Champions League success.
Asked last week about a move for the Spaniard, boss Jurgen Klopp coyly said: "I cannot end speculation as long as the transfer window is open.
"It is nice that we are linked with him but that is pretty much it really. It is because he is a good player and Liverpool is a big club, so that is nice."
However, on Thursday (17.09.20), Bayern manager Hansi Flick commented: "Thiago is an exceptional player who had huge success here for seven years.
"He's a great person and an exceptional professional. It was very emotional today when he said goodbye.