The Spain worldwide, who was in the a year ago of his deal with the Bundesliga club, arrives for an initial fee of £20million.
He's been a serial victor from his time with Barcelona and Bayern, but is now going to test himself in English football for the first time in his career and it will be intriguing to see how he deals with the physicality.
"My decision is purely sports-related", he wrote at the bottom of his message on his Twitter account alongside a video where he also bids farewell. I chose to close this chapter in this marvellous club. Triumphs, joy and also hard times. 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. "As a soccer player I want new challenges to develop myself further".
It is claimed both clubs would be interested in making the move happen, the recently relegated Watford seeing the opportunity to bring in numerous new players with the funds raised.
Thiago's contract with the Bundesliga champions was due to expire next summer and he had been linked with a move away from the club for several months.
After months of speculation about his future, Thiago finally appears set to depart treble winners Bayern and join Klopp's Premier League champions.
"Thiago is an exceptional player who spent seven hugely successful years here".
"The way he played he gave many options to the team, he was a surprising player because he solved problems in ways people did not expect". My coaching team and I enjoyed working with him.
"He's a wonderful person and an outstanding professional".
The former Scotland global played for Liverpool between 1977 and 1991, making over 400 appearances and winning eight league titles with the club where he was also captain for a spell.