Thiago, 29, joined the German giants from Barcelona in 2013 and played in last season's Champions League final victory over Paris St-Germain.
He is set to wear the number six shirt at Anfield.
Thiago would be the Premier League champions' second summer signing, after Greece left-back Kostas Tsimikas.
The guaranteed £20m will be paid in instalments, with the maximum extra £5m depending on the Reds' success in the Premier League and Champions League.
When asked about a potential move for the Spaniard last week, Liverpool manager Jurgen Klopp said: "I cannot end speculation as long as the transfer window is open.
Read more here.
