The midfielder has joined from Valencia on loan for the rest of the season and says he is delighted to have been given the chance to play in the "fantastic" Bundesliga
The Mexico midfielder has joined the German club until the end of the season with a view to penning a permanent deal in the summer.
Guardado could make his debut as early as Saturday against Stuttgart, and says he has always held German football in high regard.
"The Bundesliga has a fantastic reputation in Spain," Guardado said. "It's something special for me now to be able to play in this great European league having played in the Primera Division.
"Bayer have been a top side in German football for many years and they have also been a force in the Champions League.
"I'm therefore pleased that the transfer has worked out. This offer from Leverkusen was a great chance for me to start something new."
Bayer sporting director Rudi Voller believes Guardado, who has won 99 caps, will prove a valuable addition as manager Sami Hyypia looks to secure qualification for the Champions League.
"Andres Guardado is a very experienced player," Voller said. "Given his versatility, Andres fits the bill precisely for what we were after. We are convinced he will give our team a further boost."