Adebayor admitted his start to this year could hardly have been more different to 12 months ago.
"My dream has come true to be able to play football again at the highest level, especially with Real Madrid," he said.
"After Arsenal, when I went to Man City, don't get me wrong, it's true that I had an up and down time, and I was nearly dead as well on the way to the African Nations Cup.
"I was a little bit traumatised by all those kinds if things and it was a very difficult moment for me and today all those kinds of things are behind me.
"2010 started very badly for me, but 2011 started very well by signing a contract with Real Madrid.
"Hopefully there's a lot of good coming my way, so I have to praise God that I'm still alive and I get the chance to wear the white shirt of Real Madrid.
"I'm very honoured and very, very happy to join this club. And for all that has happened over the last six months today I'm more comfortable, more relieved and I'm very happy."
The former Arsenal forward, who scored 19 goals in 43 games for City, is not looking too far ahead.
He said: "At the moment I'm here for six months and I'm very honoured, and happy and grateful to wear Real Madrid shirt.
"The most important thing for me is to enjoy myself here and everybody is making me feel at home. I'm going to talk to the boss (Mourinho) to see how I can help the team win things.
"I'm a player who loves challenges, and who came here to achieve a lot of things.
"It's not going to be easy but I'm here to help the team achieve things."
He added: "I'm here to learn. Players never stop learning. I will learn and from then I will have to improve my game. I have to score goals, I have to create goals, I have to make things happen.
"I have to pay back all the people who have confidence in me by playing well on the pitch. Football isn't just about scoring goals - it's about attitude and what you can achieve and how you can help your team win games."