The Spain midfielder’s arrival has not been officially announced by Liverpool, but Thiago, 29, has said goodbye to Bayern in an open letter.
He is signing for least £20m, plus £5m in add-ons, on a four-year contract.
“I decided to close this chapter in this marvellous club,” Thiago wrote.
“The club where I grew and developed myself as a player during the last seven years.
“Victories, success, joy moments and some hard times as well. But what I am most proud of is having arrived in Munich being a young man full of dreams and leaving completely fulfilled and identified with a club, a history, a philosophy, a language and a culture.
“Here I learnt how to love and respect a tradition which I say goodbye now but I will never forget.”
As well as winning the Champions League with Bayern last season, Thiago has won seven consecutive Bundesliga titles, four German Cups and the Club World Cup.
He will be Premier League champions Liverpool’s second summer signing, after Greece left-back Kostas Tsimikas joined from Olympiakos.
“My decision is purely sports related,” Thiago said.
“As a football player, I want and I need new challenges in order to develop myself as I did here.”
