The 40 year-old former Liverpool, Real Madrid and Bayern Munich midfielder was announced as Gerardo Seoane's replacement.
Alonso coached Real Sociedad B for three years before departing in May and previously spent time working in Madrid's youth system.
The Leverkusen job presents a new challenge for Alonso, who inherits a side sitting 17th in the Bundesliga and third in its Champions League group after three games.
"There is of course always a risk," Alonso said at his unveiling press conference on Thursday ahead of this weekend's visit of Schalke.
"But you have to always improve and take steps forward. I firmly believe that it will work out here and I am fully motivated.
"Even as a player, I always wanted to take the right steps. I had the chance to coach good teams. But I felt I needed more time. Now I've realised that I'm ready."
Alonso confirmed "there have been inquiries" from teams in Spain but he was eager to return to Germany, where he won three Bundesliga titles in three seasons with Bayern.
"For me, things stay in my head that I feel good about from my time at Bayern," he said. "I already know about the German mentality, so that will help.
"Being here is very important for me. It's a great honour. After five years I must have forgotten some German, but I'll try my best to remember."
Leverkusen parted company with Seoane on the back of the 2-0 loss to Porto this week, which followed a 4-0 league defeat to Bayern.
It has finished in the top six in each of the past five seasons but sits inside the relegation zone with eight games played this season.
"These players have shown great quality in recent years. They should start to enjoy playing again and that way the fans will too," Alonso said.
"I've kept following the Bundesliga and the teams have gotten better. That means I had to feel even more ready. There are a lot of good coaches in this division.
"I'm hoping I can mix up the play. As a former midfielder, I like control. I want to create a winning mentality here."