He added: "It was Thiago's big wish to try something new toward the end of his career."
Liverpool are expected to sign Thiago to a four-year contract, per Ogden. The move is expected to be finalized after the Spanish midfielder passes a medical.
Thiago's transfer to the Premier League champions is believed to be worth an initial £20 million, Ogden reports. The fee will rise to £25 million if Liverpool win the Premier League or Champions League.
Manchester United were also reportedly interested in Thiago, whose contract at Bayern was set to expire next summer, but they gave up their pursuit due to the midfielder's £200,000-a-week wage demand, Ogden adds.
"I can only congratulate (Liverpool manager Jurgen) Klopp," Bayern Munich gaffer Hansi Flick said. "He not only gets a top player, but also a great person. Today, we are all very sad, and it was emotional."
Thiago joined Bayern from Barcelona in 2013. He's gone on to make over 200 appearances and win the Bundesliga title every season he's played in Germany. Thiago won the Champions League last month after Bayern beat Paris Saint-Germain in the final.
It remains to be seen whether the 29-year-old's arrival will clear the way for Georginio Wijnaldum's departure. The Liverpool midfielder has been linked with a transfer to Barcelona.
Thiago represents Liverpool's second signing of the summer after the Reds added left-back Kostas Tsimikas from Olympiacos.