Wirtz has joined the Reds for a fee rising to £125m - a British record.
Bayer chief exec Fernando Carro said: "Florian Wirtz developed from a very promising talent into a world-class player here with us. We are very proud of the path he has taken at Bayer 04. Now we have to let him go.
"We will miss Florian but part of him will always be connected to Bayer 04. His sporting ability and his irrepressible commitment are an example and inspiration to us to show our full ambition to establish Bayer 04 at the top of German football and always strive to achieve the maximum success."
Meanwhile managing director Simon Rolfes also said: "Florian's departure is associated with lots of emotions for the whole club and also for me personally. He came to us as a 16-year-old and he built up close and warm relations with many people at the club over the years. Through his attitude, his passion and his unconditional desire to win he not only motivated and inspired his teammates on the pitch but also the staff in the immediate vicinity of the team and throughout the club.
“Florian never played for himself, he always put the success of the team first. On behalf of everybody, I'd like to say a sincere thank you. Florian Wirtz will always be part of Bayer 04."