Thiago is due to undergo a medical later on Friday before sealing a move that will reportedly cost Liverpool an initial fee of £20 million ($26 million), with a further £5 million to follow in add-ons.
The 29-year-old Spain international is believed to have agreed a four-year deal with Liverpool.
He had been at Bayern since 2013 but with a year left on his contract he had stalled over signing an extension.
Thiago enjoyed a trophy-filled stay in Germany and was Bayern’s most influential player in their Champions League final victory over Paris Saint Germain last month.
In a message posted on Twitter, he said leaving Bayern had been a gut-wrenching decision.
“I have made the most difficult decision of my sports career,” Thiago wrote.
“I will close this chapter on this wonderful club where I have grown as a player for seven years. Triumphs, joy and also hard times.
“But what I am most proud of is that I arrived in Munich as a young man filled with dreams and now I will leave completely fulfilled with a club, a history and a culture.”
As well as winning the Champions League, Thiago earned seven Bundesliga titles, four German Cups and the Club World Cup during his time at Bayern.
Thiago said he had decided to leave because he wanted fresh challenges before his career ends.
“Here I learned to love a tradition that I am now saying goodbye to, but which I will never forget,” he said.
“I have experienced fantastic moments: in this city….with my Bavarian family who treated me so well and loved me every second.
“My decision is purely of a sporting nature. As a soccer player I want new challenges to develop myself further.
“Bavaria will always be my home. Thank you FC Bayern.”
Bayern boss Hansi Flick paid tribute to Thiago on Thursday.
“‘Kloppo’ (Liverpool manager Jurgen Klopp) is getting a top player and a great person,” Flick said.
“It was very emotional today when he said goodbye.”