The left-sided midfielder has joined until the end of the season with a view to penning a permanent deal come mid-year, pending his form in the Bundesliga.
The 27-year-old Mexico international could debut as early as Saturday against Stuttgart, and said 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 was thrilled his side would be aided by the experience of the 99-capped international Guardado.
"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."