Bayern and Liverpool have agreed a fee for the midfielder.
Flick says the club are disappointed to lose him, "Thiago is an extraordinary player and was very important for us.
"My coaching team and I enjoyed working with him. It was very emotional as we said goodbye. I can only congratulate Liverpool as they got a great player and especially a great person.
"Thiago gave the team a lot of options and made us unpredictable, he solved things in ways you don't expect. Now we're losing yet another great player."