"I am very grateful to Liverpool fans, they were very warm during my five years. It will be really difficult to match their appreciation," said Alonso.
"I really enjoyed those five years. But a few months ago I took that decision as I thought it was the right moment to find a fresh challenge, to look for a new club. That's when Real Madrid came along. Luckily a deal has been done and I'm very happy.
"It is a personal challenge I felt is necessary for my football career. I felt it was right so I looked for a change, for a new experience, and when Madrid came in, that's when I decided to come back to Spain."