"I am really happy to play in a team like Milan," the Switzerland international told the club's official website.
"For me, this is a dream come true. Everything has happened really fast, in a week.
"Everything here is incredible. The people are very easy going and they have made me feel like I'm at home."
Senderos, 23, paid tribute to Arsenal, the club he joined as a teenager in 2003, but believes even better times could be ahead.
"In the past I have achieved some success," he said. "To have become European Champion with the Under-17 national team and of course, at the age of 18 to have arrived to a big club as Arsenal. "In London I have learned a lot. It has been a life school and (manager Arsene) Wenger has helped me.
"Today I can say I have reached a superior level by coming to this club. I want to give 100 per cent and improve every day.
"This team wants to return to the Champions League and I will do everything I can to help."